Regge behaviour of structure functions and DGLAP evolution equation in leading order

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语言学试题及答案英语

语言学试题及答案英语一、选择题（每题2分，共20分）1. The term "phoneme" refers to:A. The smallest unit of sound in a languageB. The smallest unit of meaning in a languageC. The smallest unit of grammar in a languageD. The smallest unit of writing in a language答案：A2. Which of the following is a characteristic of the English language?A. It is a tonal languageB. It has a fixed word orderC. It has no grammatical genderD. It uses ideograms答案：B3. In linguistics, "morpheme" is defined as:A. A unit of soundB. A unit of meaningC. A unit of grammarD. A unit of writing答案：B4. The study of language change over time is known as:A. PhoneticsB. PhonologyC. SyntaxD. Historical Linguistics答案：D5. The branch of linguistics that deals with the meaning of words is called:A. SemanticsB. PragmaticsC. SyntaxD. Phonology答案：A二、填空题（每题1分，共10分）1. The study of the physical properties of speech sounds is known as ____________.答案：Phonetics2. The process of changing one language into another is known as ____________.答案：Translation3. The smallest unit of meaning in a language is called a____________.答案：Lexeme4. The study of how language is used in social contexts is known as ____________.答案：Sociolinguistics5. The study of language acquisition in children is known as ____________.答案：Child Language Acquisition三、简答题（每题5分，共20分）1. Explain the difference between a phoneme and an allophone. 答案：A phoneme is a linguistic unit that distinguishes meaning in a language, whereas an allophone is a variant of a phoneme that does not change the meaning of a word.2. What is the role of syntax in language?答案：Syntax is the set of rules, principles, and processes that govern the structure of sentences in a language, determining how words combine to form phrases, clauses, and complex sentences.3. Describe the function of morphology in language.答案：Morphology is the study of the internal structure of words and how they are formed by combining morphemes, which are the smallest meaningful units of language.4. How does sociolinguistics contribute to our understanding of language?答案：Sociolinguistics contributes to our understanding of language by examining how social factors such as class, gender, age, and ethnicity influence language variation and use in different social contexts.四、论述题（共20分）1. Discuss the importance of pragmatics in language communication.答案：Pragmatics is crucial in language communication as it deals with the study of how context influences the meaning of linguistic expressions. It helps us understand how speakersconvey intended meanings beyond the literal interpretation of words and sentences, taking into account factors such as tone, body language, and shared knowledge between speakers.2. Explain the significance of historical linguistics in understanding language evolution.答案：Historical linguistics is significant in understanding language evolution as it traces the development of languages over time, revealing how languages change, diverge, and sometimes converge. It provides insights into therelationships between languages, the migration of people, and the cultural history of language communities.。

构式语法

Development
20世纪70到80年代，Langacher 创建认知语法（构造语法）
1988年，Fillmore 提出了Construction Grammar
Kay & O’Connor(1988), Fillmore & Kay(1993), Kay & Fillmore(1999) 等也对其进行了论述
kith and kin family and friends
tickle the ivories play the piano
pull X's leg play jokes on X
例如：“What‘s the fly doing in my soup?”
显然不是询问苍蝇在做什么, 而是顾客在饭店里对所点的菜里出现苍蝇的惊讶或不满。因此, “What’s X doing Y?”的特殊用例就是构式。
Langacker和Lakoff可以被称为构式语法的先驱。 Fillmore、Kay和O’connor et al 在《语言》1988年第3期（第64卷）发表《语法构式中的规则化和习语化：以let alone为例》，他们对let alone的研究是构式语法的奠基之作，标志着构式语法的诞生。该文已经提出了“构式语法”（Construction Grammar，注意首字母是大写的
任何语言表达式, 只要它的形式、语义或功能的某些方面是不可预测( unpredictable) , 就都可称之为构式。(Goldberg, 1995)可以认为, 形式、意义和功能的不可预测性是判定构式的标准。
Let alone; all of a sudden; blue collar, white elephant 汉语中的“蓝领”“木马”“伤风”

Global Study of Nuclear Structure Functions

Global Study of Nuclear Structure Functions
S. A. Kulagin∗ Institute for Nuclear Research, 117312 Moscow, Russia R. Petti† CERN, CH-1211 Gen´ eve 23, Switzerland
arXiv:hep-ph/0412425v3 22 Oct 2005
Abstract
We present the results of a phenomenological study of unpolarized nuclear structure functions for a wide kinematical region of x and Q2 . As a basis of our phenomenology we develop a model which takes into account a number of diﬀerent nuclear eﬀects including nuclear shadowing, Fermi motion and binding, nuclear pion excess and oﬀ-shell correction to bound nucleon structure functions. Within this approach we perform a statistical analysis of available data on the ratio of the nuclear structure functions F2 for diﬀerent nuclei in the range from the deuteron to the lead. We express the oﬀ-shell eﬀect and the eﬀective scattering amplitude describing nuclear shadowing in terms of few parameters which are common to all nuclei and have a clear physical interpretation. The parameters are then extracted from statistical analysis of data. As a result, we obtain an excellent overall agreement between our calculations and data in the entire kinematical region of x and Q2 . We discuss a number of applications of our model which include the calculation of the deuteron structure functions, nuclear valence and sea quark distributions and nuclear structure functions for neutrino charged-current scattering.

不可压缩均匀各向同性湍流直接数值 1024 POF Gotoh_Fukayama_Nakano

Velocityﬁeld statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulationToshiyuki Gotoh a)Department of Systems Engineering,Nagoya Institute of Technology,Showa-ku,Nagoya466-8555,JapanDaigen FukayamaInformation and Mathematical Science Laboratory,Inc.,2-43-1,Ikebukuro,Toshima-ku,Tokyo171-0014,JapanTohru NakanoDepartment of Physics,Chuo University,Kasuga,Bunkyo-ku,Tokyo112-8551,JapanVelocityﬁeld statistics in the inertial to dissipation range of three-dimensional homogeneous steadyturbulentﬂow are studied using a high-resolution DNS with up to Nϭ10243grid points.The rangeof the Taylor microscale Reynolds number is between38and460.Isotropy at the small scales ofmotion is well satisﬁed from half the integral scale͑L͒down to the Kolmogorov scale͑␩͒.TheKolmogorov constant is1.64Ϯ0.04,which is close to experimentally determined values.The thirdorder moment of the longitudinal velocity difference scales as the separation distance r,and itscoefﬁcient is close to4/5.A clear inertial range is observed for moments of the velocity differenceup to the tenth order,between2␭Ϸ100␩and L/2Ϸ300␩,where␭is the Taylor microscale.Thescaling exponents are measured directly from the structure functions;the transverse scalingexponents are smaller than the longitudinal exponents when the order is greater than four.Thecrossover length of the longitudinal velocity structure function increases with the order andapproaches2␭,while that of the transverse function remains approximately constant at␭.Thecrossover length and importance of the Taylor microscale are discussed.©2002AmericanInstitute of Physics.͓DOI:10.1063/1.1448296͔I.INTRODUCTIONKolmogorov studied the statistical laws of a velocity ﬁeld for small scales of turbulent motion at high Reynolds numbers.1,2Two hypotheses were introduced in his theory ͑hereafter K41for short͒:local isotropy and homogeneity exists;and there is an inertial range in the energy spectrum of theﬂow that is independent of viscosity and large-scale properties at sufﬁciently high Reynolds numbers.The most prominent conclusion of his theory is the presence of the Kolmogorov spectrum E(k)ϭK⑀¯2/3kϪ5/3in the inertial range,where⑀¯is the average rate of energy dissipation per unit mass and K is a universal constant.Since K41,there has been a considerable amount of ef-fort made to study the turbulent velocityﬁeld statistics in the inertial range,and the energy spectrum has been a central quantity of interest.The Kolmogorov spectrum and constant have been measured inﬁeld and laboratory experiments.3–7 The exponent for the inertial range spectrum is now widely accepted asϪ5/3,with a small correction to account forﬂow intermittency.The Kolmogorov constant K is between1.5 and 2.After studying the results of many experiments, Sreenivasan stated that K is1.62Ϯ0.17.7The spectral theory of turbulence has also been used to predict the Kolmogorov constant.The value of K is1.77when the Lagrangian history direct interaction approximation͑LHDIA͒is used,8,9and 1.72when the Lagrangian renormalized approximation ͑LRA͒is used.10,11These are fully systematic theories that do not contain any ad hoc parameters.Direct numerical simulations͑DNSs͒of turbulentﬂows are now performed at higher Reynolds numbers,due to the recent dramatic increase in computational power.In the early 90’s,the resolution of DNS reached Nϭ5123grid points with a Taylor microscale Reynolds number R␭of 210ϳ240.12–20Most high-resolution DNSs have been per-formed for steady turbulence conditions to achieve high Rey-nolds numbers and obtain reliable statistics.Although results were reported with R␭greater than200,an inertial range spectrum was observed only for the lowest narrow wave number band at which forcing was applied.The Kolmogorov constant was inferred to be about1.5ϳ2in Ref.14and1.62 in Ref.16,but these results are not convincing,due to the insufﬁcient width of the scaling range,anisotropy of theﬂow ﬁeld,limited ensemble size,forcing techniques used,and numerical limitations of the simulations.Intermittency has also attracted the interest of research-ers.Since Kolmogorov’s intermittency theory͑hereafter K62͒,21many theoretical and statistical models of intermit-tency have been developed.4,22,23The scaling exponents of higher order structure functions for velocity differences in the inertial range were studied intensively.Intermittency in-creases with a decrease in the size of the scales of motion. The small-scale statistics gradually deviate from a Gaussian distribution,and the scaling exponents differ from those pre-dicted by K41.Experiments at very high Reynolds numbers have beena͒Electronic mail:gotoh@system.nitech.ac.jpPHYSICS OF FLUIDS VOLUME14,NUMBER3MARCH200210651070-6631/2002/14(3)/1065/17/$19.00©2002American Institute of Physicsperformed in the atmospheric boundary layer and in huge wind tunnels,and the measured scaling exponents were found to deviate from K41scaling.5,6,24,25,84However,there have been arguments made about the lack of small-scaleﬂow isotropy and homogeneity in these experiments,which might be affected by the large-scale shear.25,26For experiments at moderate Reynolds numbers under relatively well-controlled laboratory conditions,the width of the scaling range is usually not large enough to determine the scaling exponents precisely.Extended self-similarity͑ESS͒has been exploited to overcome this difﬁculty and applied to various turbulentﬂows in both experiments and DNSs.28–31 The idea is to measure the scaling exponents of the structure functions when they are plotted against the third order lon-gitudinal structure function,rather than to use the separation distance.The width of the scaling range is longer than that obtained with the usual method at low to moderate Reynolds numbers.The scaling exponents are anomalous,but do agree with those obtained from high Reynolds number experiments up to a certain order.24,28–31However,there is no consensus as to why the structure functions give a longer inertial range, or what is missing from theﬂow statistics as a result.Also, there is no unique way to determine the scaling exponents for the transverse and mixed velocity structure functions,be-cause those higher order structure functions can be plotted against other types of third order structure functions as well as the third order longitudinal structure function.There also have been arguments about whether the scal-ing exponents for the longitudinal and transverse structure functions at small scales are equal.25–27,32–38Many experi-ments and DNSs have reported that higher order longitudinal scaling exponents are larger than transverse ones.However, some researchers have argued that the difference is due to deviation from the assumed conditions,such as local homo-geneity,isotropy,and the independence of small scales from macroscale parameters.They have suggested that when the Reynolds number becomes large enough,the difference will vanish.36,37,39,40In many aspects of turbulence research,there have been questions posed about the extent to which the local homoge-neity and isotropy of the turbulent velocityﬁeld are attained. This will affect the small-scale statistics signiﬁcantly.Recent experimental studies have shown that local isotropy is par-tially satisﬁed for lower order moments.25,26,37However,it is not sufﬁcient to examine only the conditions assumed in the above studies,and only a limited knowledge of the trueﬂow conditions is available so far.26,37,38A DNS with a sufﬁciently large grid size provides abetter opportunity to examine the points raised above.It hasthe advantage that any physical quantity can be measureddirectly without deforming theﬂowﬁeld.In the presentstudy,a series of large scale DNSs have been performed at ahigh resolution of up to Nϭ10243and R␭ϭ460.41–45The inertial range of the turbulenceﬁeld has a considerablelength,and useful velocity statistics can be extracted such asthe Kolmogorov constant,the energy spectrum,velocitystructure functions up to the tenth order,their scaling expo-nents,and probability density functions for velocity differ-ences.To the authors’best knowledge,these are theﬁrstDNS data in the inertial range;the data provide new insightinto the inertial and dissipation ranges.The main purposes of the present paper are to describethe statistics of the velocityﬁeld in an incompressible steadyturbulentﬂow obtained from the DNS,and to reexaminecurrent knowledge of turbulence,developed since K41.Thepaper is organized as follows.The numerical aspects of thepresent DNS are described in Sec.II,and the energy spec-trum is examined in Sec.III.The variation of single pointquantities and probability density functions͑PDFs͒with theReynolds number is discussed in Sec.IV.The isotropy of thesecond and third order moments of the velocity difference isexamined in Sec.V,and the energy budget is examined interms of the Ka´rma´n–Howarth–Kolmogorov equation inSec.VI.The structure functions and scaling exponents arediscussed in Sec.VII.Section VIII presents an analysis ofthe crossover lengths of the structure functions.Finally,asummary and conclusions are provided in Sec.IX.II.NUMERICAL SIMULATIONThe Navier–Stokes equations are integrated in Fourierspace for unit density:ͩץץtϩ␯k2ͪuϭP͑k͒•F͓uÃ␻͔kϩf,͑1͒͗f͑k,t͒f͑Ϫk,s͒͘ϭP͑k͒F͑k͒4␲k2␦͑tϪs͒,͑2͒where␻is the vorticity vector,P͑k͒is the projection opera-tor,F denotes a Fourier transform,and f is a solenoidal Gaussian random force that is white in time.The spectrum of the random force F(k)is constant over the low wave number band and zero otherwise;the force is normalized asTABLE I.DNS parameters and statistical quantities of the runs.T eddya v is the period used for the time average.R␭N k max␯c f Forcing range T eddya v E⑀¯L␭␩(ϫ10Ϫ2)K 38128360 1.50ϫ10Ϫ2 1.30ͱ3рkрͱ1222.6 1.99 1.190.8910.501 4.10¯5425631217.00ϫ10Ϫ30.70ͱ3рkрͱ1214.9 1.390.6270.8290.393 2.72¯702563121 4.00ϫ10Ϫ30.50ͱ3рkрͱ1249.7 1.160.4570.7850.318 1.93¯1255123241 1.35ϫ10Ϫ30.50ͱ3рkрͱ12 5.52 1.250.4920.7440.1850.841¯2845123241 6.00ϫ10Ϫ40.501рkрͱ6 3.03 1.960.530 1.2460.1490.449 1.64 38110243483 2.80ϫ10Ϫ40.511рkрͱ6 4.21 1.740.499 1.1390.09890.258 1.63 46010243483 2.00ϫ10Ϫ40.511рkрͱ6 2.14 1.790.506 1.1500.08410.199 1.64 1066Phys.Fluids,Vol.14,No.3,March2002Gotoh,Fukayama,and Nakano͵ϱF ͑k ͒dk ϭ⑀¯in ,͑3͒where ⑀¯in is the average rate of the energy input per unit mass.A pseudo-spectral code was used to compute the con-volution sums,and the aliasing error was effectively re-moved.The time integration was performed using the fourth order Runge–Kutta–Gill method.Physical quantities of turbulent ﬂow include the total energyE ͑t ͒ϭ12͗u 2͘ϭ32u ¯2ϭ͵ϱE ͑k ͒dk ,͑4͒the average energy dissipation per unit mass⑀¯ϭ2␯͵ϱk 2E ͑k ͒dk ,͑5͒the integral scaleL ϭͩ3␲4͵ϱk Ϫ1E ͑k ͒dkͪͲE ,͑6͒the Taylor microscale␭ϭͩ5EͲ͵ϱk 2E ͑k ͒dkͪ1/2,͑7͒the Taylor microscale Reynolds numberR ␭ϭu ¯␭␯,͑8͒and the Kolmogorov scale␩ϭͩ␯3⑀¯ͪ1/4.͑9͒The range of the Taylor microscale Reynolds number was 38to 460.The characteristic parameters of the DNS are listed in Table I.43Most of these are identical to Gotoh and Fukayama,43but the averaging time for R ␭ϭ381was ex-tended to 4.21large eddy turnover times.A statistically steady state was conﬁrmed by observing the time evolutionof the total energy,the total enstrophy,and the skewness of the longitudinal velocity derivative.The statistical averages were computed as time averages over tens of large eddy turnover times for the lower Reynolds number ﬂows,and over a few large eddy turnover times for the higher Reynolds number ﬂows.The resolution condition k max ␩Ͼ1was satis-ﬁed for most runs,except for R ␭ϭ460in which k max ␩was slightly less than unity (k max ␩ϭ0.96).This does not ad-versely affect the results in the inertial range.The computational time required for runs at a N ϭ10243resolution varied,depending on the statistical data that was gathered.Typically,60h was required for one large eddy turnover time.The total time of the computations was more than 500h for the longest run (R ␭ϭ381).Data col-lected during the transition period to steady state ͑about six large eddy turnover times ͒were discarded.The relatively long time required to attain steady state was due to the low wave number band forcing.This imposes a severe computa-tional putations with R ␭р284were per-formed on a Fujitsu VPP700E parallel vector machine with 16processors at RIKEN.Simulations of higher R ␭were per-formed on a Fujitsu VPP5000/56with 32processors at the Nagoya University Computation Center.III.ENERGY SPECTRUMFigure 1shows the three-dimensional energy spectrum calculated for each run.All of the curves are scaled to the Kolmogorov units and multiplied by k 5/3.As the Reynolds number increases,the curves extend toward lower wave numbers.The curves of ﬂows with Reynolds numbers larger than R ␭ϭ284contain a ﬁnite plateau,which indicates that E (k )ϰk Ϫ5/3.There is a bump when 0.04рk ␩р0.3at the high end of the inertial range,which is consistent with pre-vious experimental and numerical observations.6,16The nor-malized energy transfer ﬂux,deﬁned by1⑀¯⌸͑k ͒ϭ1⑀¯͵kϱT ͑k Ј͒dk Ј͑10͒is shown in Fig.2,where T (k )is a nonlinear energy transfer function in the energy spectrum equation.4,22Between0.007рk ␩р0.04,⌸(k )/⑀¯is approximately constantand FIG.1.Scaled energy spectra,⑀¯Ϫ1/4␯Ϫ5/4(k ␩)5/3E (k ).The inertial range is 0.007рk ␩р0.04and K ϭ1.64Ϯ0.04.A horizontal line indicates K ϭ1.64.FIG.2.Normalized energy transfer ﬂux,⌸(k )/⑀¯for R ␭ϭ381and 460.1067Phys.Fluids,Vol.14,No.3,March 2002Velocity ﬁeld statistics in homogeneousclose to unity;thus the ﬂow is in an equilibrium state over the inertial range of the energy spectrum,corresponding to the plateaus in Fig.1.The Kolmogorov constant given in Table I is determined using a least square ﬁt between 0.007рk ␩р0.04on the R ␭Ͼ284curves.In Ref.43,the Kolmog-orov constant was reported as K ϭ1.65Ϯ0.05.However,the averaging time has since been extended for the R ␭ϭ381run.The R ␭ϭ478run differs slightly from statisticalequilibrium,since ⌸(k )/⑀¯is not exactly one;for this reason,the R ␭ϭ478data were not used for this analysis.The Kol-mogorov constant,computed using the data only from the R ␭ϭ381and 460runs,isK ϭ1.64Ϯ0.04,͑11͒which is in good agreement with experimental values and recent DNS data.7,16There are many DNSs reporting the Kolmogorov constant higher than the value 1.64.However,the length of the inertial range in those DNSs is not long enough to clearly observe the k Ϫ5/3range,and the top of the bump of the compensated energy spectrum k 5/3E (k )is un-derstood as the inertial range,so that the Kolmogorov con-stant is read as about 2as seen in Fig.1.16The Kolmogorov constant 1.64is also close to the value obtained using the LHDIA ͑1.77͒,8,9the LRA ͑1.72͒.10,11These spectral theories of turbulence are consistent with Lagrangian dynamics,arederived systematically,and contain no ad hoc parameters.Figure 3shows the one-dimensional energy spectrum ob-tained from the present DNS with R ␭ϭ460,from experi-ments,and from the LRA.The agreement between the curves is satisfactory.Therefore we conclude that the present DNS has successfully calculated a homogeneous turbulent ﬂow ﬁeld in the inertial range of the energy spectrum.IV.ONE-POINT STATISTICS A.MomentsSome one-point moments of the velocity ﬁeld areS 3͑u ͒ϵ͗u 3͗͘u 2͘3/2,S 3͑u x ͒ϵ͗u x 3͗͘x 2͘3/2,͑12͒K 4͑u ͒ϵ͗u 4͗͘u 2͘2,K 4͑u x ͒ϵ͗u x 4͗͘u x 2͘2,K 4͑u y ͒ϵ͗u y 4͗͘u y 2͘2,͑13͒where u is the velocity component in the x direction.The variation of these moments with the Reynolds number is shown in Fig.4and listed in Table II.The general behavior of the curves is consistent with previous DNS and experi-mental data.13,14,18,19,26,46,47There are small effects of rela-tively low resolution on S 3and K 4for the velocity deriva-tives for R ␭ϭ381and 460data.The skewness factor of the velocity u is very small for runs with the R ␭р125,and isofparison of one-dimensional energy spectra.Symbols:experi-ments,solid line:present DNS (R ␭ϭ460),dashed line:statistical theory ͑LRA and MLRA ͒.FIG.4.Variation of the moments of the velocity and velocity gradient withthe Reynolds number.Line:present DNS,circle:K 4(u y )͑Jime´nez et al.,Ref.13͒,solid square:K 4(u )͑Jime ´nez et al.,Ref.13͒,square:K 4(u x )͑Wang et al.,Ref.14͒,plus:K 4(u x )͑Vedula and Yeung,Ref.18͒,star:ϪS 3(u x )͑Wang et al.,Ref.14͒.TABLE II.Moments of the velocity and velocity derivatives.R ␭S 3(u )K 4(u )S 3(ץu /ץx )K 4(ץu /ץx )K 4(ץu /ץy )380.0227 2.89Ϫ0.520 4.14 5.16540.00563 2.86Ϫ0.517 4.47 6.00700.00473 2.93Ϫ0.519 4.81 6.621250.0820 2.94Ϫ0.529 5.658.192840.0231 2.77Ϫ0.531 6.6310.1381Ϫ0.246 2.98Ϫ0.5747.9012.2460Ϫ0.1682.89Ϫ0.5457.9111.71068Phys.Fluids,Vol.14,No.3,March 2002Gotoh,Fukayama,and Nakanothe order of 0.2for runs with the R ␭у284.The relatively large values of the velocity skewness are caused by the shorter averaging time used compared to the low Reynolds number runs.Since most of the energy resides in the lowest wave number band,there are persistent large ﬂuctuations of the large scales of motion over longer time period.The longer time average or the forcing at larger wave numbers would yield smaller velocity skewness.The ﬂatness factor of the velocity ﬁeld is close to three,which is the Gaussian value.The skewness factor of the longitudinal velocity deriva-tives is very insensitive to the Reynolds number,S 3͑u x ͒ϰR ␭0.0370,͑14͒where the exponent is determined by a least square ﬁt.Theaverage value is Ϫ0.53,which is consistent with experimen-tal observations over the range of Reynolds numbers studied in the present work.However,the exponent is smaller than indicated by the experimental data.26,46The ﬂatness factors for the longitudinal and transverse velocity derivatives in-crease with the Reynolds number asK 4͑u x ͒ϰR ␭0.266,K 4͑u y ͒ϰR ␭0.335.͑15͒The exponent of K 4(u y )is larger than that of K 4(u x );thus,the PDF for the transverse velocity derivative has longer tails than those of the longitudinal velocity derivative.From ex-perimental observations,Shen and Warhaft reported thatK 4(u x )ϰR ␭0.37and K 4(u y )ϰR ␭0.25.26Since there is scatter in the experimetal data,the exponents in Eq.͑15͒by the present DNS are not inconsistent with the experimental data.Van Atta and Antonia studied the Reynolds number dependence of S 3(u x )and K 4(u x ),46and found thatS 3͑u x ͒ϰR ␭0.12,K 4͑u x ͒ϰR ␭0.32for ␮ϭ0.2,͑16͒S 3͑u x ͒ϰR ␭0.15,K 4͑u x ͒ϰR ␭0.41for ␮ϭ0.25,͑17͒where ␮is the exponent deﬁned by ͗⑀r 2͘ϰr Ϫ␮for the locally averaged energy dissipation rate.4,21Generally,the Reynolds number dependency of S 3and K 4in our DNSs is weaker than observed in the experiments,irrespective of the type of forcing used.We believe this is because the range of Rey-nolds numbers in DNS is smaller than experimental ﬂows,and there remain small-scale anisotropy effects in the experi-ments.B.Probability density functionsThe probability density function conveys information about single-point velocity statistics.It has been one of the central issues of turbulence research in the last decade.Single-point PDFs for the velocity and its derivatives are shown in Figs.5–7.A longer time period was necessary for the time average to obtain well-converged PDF for the ve-locity Q (u ).The distribution Q (u )is close to Gaussian,and its tail extends to very low values of the order of 10Ϫ10.Such values have not been reported in the literature.The Q (u )curve for R ␭ϭ381is skewed negatively,but this is attributed to the insufﬁcient time-averaging period ͑four large eddy turnover times ͒that was used.The overall trend is that Q (u )decays faster than a Gaussian distribution at large ampli-tudes.This behavior was also observed in one-dimensional decaying and forced Burgers turbulence.48,49Jime´nez has shown that the PDF Q (u )is slightly sub-Gaussian as the energy spectrum decays faster than k Ϫ1.50FIG.5.Variation of velocity PDF with the Reynoldsnumber.FIG.6.Variation of the longitudinal velocity derivative PDF with the Rey-noldsnumber.FIG.7.Variation of the transverse velocity derivative PDF with the Rey-nolds number.1069Phys.Fluids,Vol.14,No.3,March 2002Velocity ﬁeld statistics in homogeneousThis is consistent with the present DNS results.Studies of the Q (u )tail predict that Q (w )ϰexp(Ϫc ͉w ͉3)when the forc-ing has a short correlation time.51,52Here,w ϭu /͗u 2͘1/2is the normalized velocity amplitude and c is a nondimensional constant.The asymptotic form of Q (u )was examined by plotting ln ͓Ϫln(Q (w )͔against ln ͉w ͉;however,the Q (w )tails were too short to determine the true asymptotic form.The PDF for the longitudinal velocity derivative is slightly skewed,as expected from the ﬁnite negative value of the skewness factor.The tail becomes longer as the Reynolds number increases.Figure 7shows that the PDF of the trans-verse derivative is symmetric and has a longer tail than the longitudinal derivative.There are many theories for the PDF of the velocity derivative.The asymptotic tail of Q (ץu /ץy )is presented in Fig.8,in which both the positive and negative sides are plotted by assuming that the PDF is symmetric.The tails gradually become longer as the Reynolds number increases;therefore,Q (s )is Reynolds-number dependent,and cannot be represented in a single stretched exponential form as Q (s )ϰexp(Ϫb ͉s ͉h ),where s is the normalized amplitude of ץu /ץy and b is a nondimensional constant that is a function of the Reynolds number.53V.ISOTROPYThe hypothesis of isotropy of the ﬂow ﬁeld is one of the key components of K41.There are various methods to ex-amine the degree of isotropy.One measure of isotropy can be obtained from the relations between the second and third order longitudinal and transverse velocity structure func-tions.These areD LL ϵ͗͑␦u r ͒2͘,D TT ϵ͗͑␦v r ͒2͘,͑18͒D LLL ϵ͗͑␦u r ͒3͘,D LTT ϵ͗␦u r ͑␦v r ͒2͘,͑19͒where␦u r ϵ͑u ͑x ϩr ͒Ϫu ͑x ͒͒•r /r ,͑20͒␦v r ϵ͑u ͑x ϩr ͒Ϫu ͑x ͒͒•͑I Ϫrr /r 2͒•e Ќ,͑21͒and e Ќis the unit vector perpendiculer to r ,and I is the unit tensor.Then the isotropy and incompressibility relations areD TT ͑r ͒ϭD LL ͑r ͒ϩr 2dD LL ͑r ͒dr ,͑22͒D LTT ͑r ͒ϭ16ddrrD LLL ͑r ͒.͑23͒In DNS,the solenoidal property of the Fourier amplitude velocity vector u ͑k ͒is always satisﬁed to the level of nu-merical error,which is smaller than 10Ϫ15.Thus,the accu-racy of the above relations depends solely on the deviation from isotropy.The two sides of Eqs.͑22͒and ͑23͒are com-pared for R ␭ϭ125,381,and 460in Figs.9and 10.The curves in the ﬁgures are divided by r 2/3and r ,respectively,and the vertical axes of the plots are linear.The thick lines represent the left hand sides of Eqs.͑22͒and ͑23͒,and the thin lines correspond to the right-hand sides.The isotropy of the second and third order moments is excellent for scales less than L /2.The difference at larger separations is caused by the anisotropy due to the small number of energy-containing Fourier modes.The curves for R ␭ϭ381and460FIG.8.Variation of the asymptotic tail of the transverse velocity derivative PDF with the Reynolds number.Both positive and negative sides are plot-ted.The rightmost curve corresponds to R ␭ϭ460.FIG.9.Isotropy relation at the second order.Thin line:D TT (r )r Ϫ2/3,thick line:(D LL (r )ϩ(r /2)(dD LL (r )/dr ))r Ϫ2/3.L /␩and ␭/␩are shown for R ␭ϭ460.FIG.10.Isotropy relation at the third order.Thin line:D LTT (r )r Ϫ1,thick line:((1/6)(d /dr )rD LLL (r ))r Ϫ1.L /␩and ␭/␩are shown for R ␭ϭ460.1070Phys.Fluids,Vol.14,No.3,March 2002Gotoh,Fukayama,and Nakanoin Fig.9are not horizontal,suggesting that the second order structure function does not scale as r 2/3.The scaling expo-nents will be examined later in this paper.The isotropic re-lations,such as D 1122ϭD 1133and D 2222ϭ3D 2233ϭD 3333,and Hill’s higher order relations were not computed.54VI.KA´RMA ´N–HOWARTH–KOLMOGOROV EQUATION The energy budget for various scales is described by the Ka´rma ´n–Howarth–Kolmogorov ͑KHK ͒equation,45⑀¯r ϭϪD LLL ϩ6␯ץD LL ץrϩZ ͑24͒for steady turbulence,4,55,56where Z (r )denotes contributions due to the external force given by Z ͑r ,t ͒ϭ͵Ϫϱt͗␦f ͑r ,t ͒•␦f ͑r ,s ͒͘dsϭ12r͵0ϱͩ115ϩsin kr ͑kr ͒3ϩ3cos kr ͑kr ͒4Ϫ3sin kr ͑kr ͒5ͪF ͑k ͒dk .͑25͒Since the external force spectrum F (k )is localized in arange of low wave numbers,the asymptotic form of Z (r )for small separations is given asZ ͑r ͒ϭ235⑀¯in k f 2r 3,k f 2ϵ͐0ϱk 2F ͑k ͒dk͐0ϱF ͑k ͒dk.͑26͒A generalized Ka´rma ´n–Howarth–Kolmogorov equation has also been derived:57–6343⑀¯r ϭϪ͑D LLL ϩ2D LTT ͒ϩ2␯ץץr͑D LL ϩ2D TT ͒ϩW ,͑27͒where W ͑r ͒ϭ4r͵0ϱͩ13ϩcos kr ͑kr ͒2Ϫsin kr͑kr ͒3ͪF ͑k ͒dk ,Ϸ215⑀¯in r 3k f 2for ͉k f r ͉Ӷ1.͑28͒Equation ͑24͒is recovered by substituting Eqs.͑22͒and ͑23͒into Eq.͑27͒.Figure 11shows the results obtained when each term of Eq.͑24͒is divided by ⑀¯r for R ␭ϭ460.Curves in which r /␩is larger than r /␩ϭ1200are not shown,because the sign of D LLL changes.A thin horizontal line indicates the Kolmog-orov value 4/5.When the separation distance decreases,the effect of the large scale forcing used in the present DNS decreases quickly,while the viscous term grows gradually.The third order longitudinal structure function D LLL quickly rises to the Kolmogorov value,remains there over the iner-tial range ͑between r /␩Ϸ50and 300͒,and then decreases.In the inertial range,the force term decreases as r 3according to Eq.͑26͒,while the viscous term increases as r ␨2Ϫ1(␨2Ͻ1)when r decreases.͓Since each term in the ﬁgure is divided by (⑀¯r ),the slope of each curve is 2and ␨2Ϫ2,respectively.͔The sum of the three terms in the right hand side of Eq.͑24͒divided by ⑀¯r is close to 4/5,the Kolmogorov value.The deviation of the sum from the 4/5law at the smallest scales is due to the slightly lower resolution of the data at these scales ͑k max ␩is close to one ͒.At larger scales greater than r /␩ϭ700,the deviation is caused by the ﬁniteness oftheFIG.11.Terms in the Ka´rma ´n–Howarth–Kolmogorov equation when R ␭ϭ460.Thin solid line:4/5.FIG.12.Kolmogorov’s 4/5law.L /␩and ␭/␩are shown for R ␭ϭ460.The maximum values of the curves are 0.665,0.771,0.781,and 0.757for R ␭ϭ125,284,381,and 460,respectively.FIG.13.Terms in the generalized Ka´rma ´n–Howarth–Kolmogorov equation for R ␭ϭ460.Thin solid line:4/3.1071Phys.Fluids,Vol.14,No.3,March 2002Velocity ﬁeld statistics in homogeneousensemble,which indicates the persistent anisotropy of the larger scales.The above ﬁndings are consistent with the cur-rent knowledge of turbulence developed since Kolmogorov,although conﬁrmation of some aspects of turbulence using actual data is new from both a numerical and experimental point of view.56,59–65It is interesting and important to observe when the Kol-mogorov 4/5law is satisﬁed as the Reynolds numberincreases.6,66–69Figure 12shows curves of ϪD LLL (r )/(⑀¯r )for various Reynolds numbers.In this ﬁgure,the 4/5law applies when the curves are horizontal.The portion of the curves in which r /␩Ͼ1200is not shown.Although there is a small but ﬁnite horizontal range when R ␭Ͼ284,the level of the plateau is still less than the Kolmogorov value.The maximum values of the curves are 0.665,0.771,0.781,and 0.757for R ␭ϭ125,284,381,and 460,respectively.The value 0.781for R ␭ϭ381is 2.5%less than 0.8.An asymptotic state is approached slowly,which is consistent with recent studies.However,the asymptote is approached faster than predicted by the theoretical estimate.66,69Theslow approach is due to the fact that D LLL (r )is the third order structure function and most positive contributions are canceled by negative ones.Thus only the slight asymmetry of the ␦u r PDF contributes to D LLL .The level of the plateau of the R ␭ϭ460curve is slightly less than the others.A higher value would be expected if the time average period used for the R ␭ϭ460run were longer.The generalized Ka´rma ´n–Howarth–Kolmogorov equa-tion Eq.͑27͒is also examined in a similar fashion.Figure 13shows each term of the equation divided by ⑀¯r ;a horizontal line indicates the 4/3law.The agreement between the present data and theory is satisfactory.The third order moment slowly approaches the Kolmogorov value 4/3,as shown in Fig.14.The maximum values of the curves of the 4/3law are 0.564,1.313,1.297,and 1.259for R ␭ϭ125,284,381,and 460,respectively.VII.STRUCTURE FUNCTIONS AND SCALING EXPONENTSThe velocity structure functions are deﬁned asS p L ͑r ͒ϭ͉͗␦u r ͉p͘,S p T ͑r ͒ϭ͉͗␦v r ͉p͘,FIG.14.Kolmogorov’s 4/3law.L /␩and ␭/␩are shown for R ␭ϭ460.The maximum values of the curves for the 4/3law are 0.564,1.313,1.297,and 1.259for R ␭ϭ125,284,381,and 460,respectively.FIG.15.Variation of the ␦u r PDF with r for R ␭ϭ381.From the outermostcurve,r n /␩ϭ2n Ϫ1dx /␩ϭ2.38ϫ2n Ϫ1,n ϭ1,...,10,where dx ϭ2␲/1024.The inertial range corresponds to n ϭ6,7,8.Dotted line:Gaussian.FIG.16.Variation of PDF for ␦v r with r at R ␭ϭ381.The classiﬁcation of curves is the same as in Fig.17.FIG.17.Convergence of the tenth order accumulated moments C 10(␦u r )at R ␭ϭ381for various separations r n /␩ϭ2.38ϫ2n Ϫ1,n ϭ1,...,10.Curves are for n ϭ1,...10from the uppermost,and the inertial range corresponds to n ϭ6,7,8.1072Phys.Fluids,Vol.14,No.3,March 2002Gotoh,Fukayama,and Nakano。

Creep behavior of austenitic stainless steel weld metals as a function of ferrite content

Materials Science and Engineering A452–453 (2007) 284–291Creep behavior of austenitic stainless steel weldmetals as a function of ferrite contentY.Cui∗,Carl D.LundinDepartment of Materials Science and Engineering,The University of Tennessee,Knoxville,TN37996-2200,USAReceived26July2005;received in revised form17October2006;accepted18October2006AbstractFour types of modiﬁed and commercial E308H and E316H weld deposits with Ferrite Number(FN)in the range of0–5.7were investigated for creep behavior at stress levels between70and240MPa,with a range of temperature550–700◦C.After creep testing,sigma phase was found in commercial E308H and E316H creep samples,signiﬁcant carbide evolution from modiﬁed E308H and E316H with0FN creep samples distribute in a random and a chain along the substructures and grain boundaries,respectively.The creep results show that,for E316H weld deposits,modiﬁed samples with0FN,even though containing microﬁssures,have a higher creep strength than theﬁssure-free commercial samples with a higher ferrite content.This can be attributed to the beneﬁcial effect from the carbides on dislocation barriers and the detrimental effect on hard and brittle sigma formed in commercial E316H.Fissure-containing modiﬁed E308H has a lower creep strength thanﬁssure-free commercial sample because of the propagation paths provided byﬁssures and the minimal effect on the randomly distributed carbides.© 2006 Elsevier B.V. All rights reserved.Keywords:Welding;Creep;Austenitic stainless steel;Ferrite Number;Dislocation1.IntroductionAustenitic stainless steels constitute the largest stainless fam-ily in terms of alloy type and are used in various corrosive conditions over the temperatures ranging from cryogenic to elevated[1].They are generally regarded as readily weldable materials without the risk of cracking and with considerable tolerance for variations in welding conditions.However,fully austenitic weld deposits may contain microﬁssures in single pass welds and in underlying weld runs reheated by subsequent passes in multipass welds.The occurrence of the microﬁssures can be the cause of weld rejection and may induce of prop-erty degradation of the weld metal.Hot cracking in austenitic stainless steel welds has been extensively discussed in the lit-erature,and a universal agreement,on liquidation mechanisms, have been reached among investigators[2–10].Carl D.Lundin summarized the characteristics of microﬁssuring in his series of articles discussing microﬁssure investigations.Microﬁssures occur primarily in ferrite-free areas along grain boundaries in the HAZ of the previous deposited weld pass.The microﬁs-∗Corresponding author.Tel.:+18659745299;fax:+18659740880.E-mail address:ycui1@(Y.Cui).suring tendency is enhanced by multiple thermal cycling in the HAZ[11].In addition,a low ductility region already exists in the weld metal of previously deposited weld beads from multi-pass or repair welding.This region is usually the initial location for microﬁssuring occurrence when the weld with a low ferrite content,under a high imposed strain that exceeds the strain tol-erance of the microstructure[9].Delta ferrite is usually required at a certain level for its beneﬁcial effect in reducing or preventing microﬁssuring in austenitic stainless steel weldments[12].This level of ferrite was moreﬁrmly established by Lundin et al.in an article documenting the ferrite-ﬁssuring tendency of austenitic stainless steel weld metals[13].Because the microﬁssures are very small and not detectable at lower magniﬁcation,the Fissur-ing Bend Test method is often used to evaluate the microﬁssuring tendency in multipass weldments due to its favorable features most desired in a weldability test[18].Several of constitution diagrams and models have been developed to accurately predict the ferrite content in stainless steel welds[14–17].Electrode manufacturers as well as consumers often use Ferrite Number,a measure of the ferrite content,as an alloy speciﬁcation in order to ensure that weldments contain a desired minimum(or maxi-mum)ferrite level.Ferrite in the austenitic stainless steel weld plays a dual role.On the one hand,it reduces the susceptibility of the weld to hot cracking and on the other hand it affects the0921-5093/$–see front matter© 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2006.10.132Y.Cui,C.D.Lundin/Materials Science and Engineering A 452–453 (2007) 284–291285creep properties for long-term service at elevated temperatures. Microﬁssures can be controlled to a certain extent by attention to consumable composition and purity,and welding technique, but they cannot be uniquely eradicated in real weld application because ferrite distribution is not uniform.Thus,Ferrite Num-ber and microﬁssures or cracks in austenitic materials generally cause the most alarm when the weldment properties are being considered such as strength,toughness,corrosion resistance and long-term service at elevated temperatures.The purpose of this study was to evaluate the creep behavior of austenitic stainless steel weld metals with and without ferrite content(ﬁssure-free andﬁssure-containing).2.Experimental procedures2.1.Materials evaluationFour different weld electrodes(3.2mm diameter),com-mercial and modiﬁed E308H and E316H,were used in this investigation.Modiﬁed electrodes are those electrodes that were especially produced by adjusting the ratio of Chromium-equivalent and Nickel-equivalent in order to obtain a ferrite-free microstructure and produce microﬁssures.The deposit chemical compositions still meet the AWS A5.4speciﬁcation,as shown in Table1.The base metal used is304stainless steel cut from bar stock.Three-layer weld pads(six beads to each layer)were pro-duced using Shielded Metal Arc(SMA)welding to permit the evaluation of microﬁssuring in relatively undiluted weld metal. Before welding,plates were clamped on each end to a heavy backingﬁxture to prevent excessive deformation during weld-ing.The deposited three-layer pad is approximately6.4mm thick,25.4mm wide and203mm long with the conﬁguration as shown in Fig.1.The welding parameters are shown in Table2. With the pads still in the clampingﬁxture,the surface was milled using a0.254mm depth of cut on each pass until the surface was clear of irregularities.The pad surface was ground on a surface grinder using a12pass sequence with theﬁrst8passes each removing0.025mm and theﬁnal4passes each removing 0.013mm.After grinding,the specimens were removed from the clampingﬁxture and ultrasonically washed in methanol to remove all traces of cuttingﬂuids for Ferrite Number measure-ment and Fissure Bend Testing.The Ferrite Number was determined in the center100mm region of the ground pad,using a15intersection grid layout, with the Feritscope,as shown in Fig.2.The average Ferrite Number of commercial E316H and E308H,modiﬁed E316H and E308H are4.7,5.7,0and0,respectively.Fig.1.Schematic drawing of(a)the clampingﬁxture and(b)the pad conﬁgu-ration.Table2Welding parametersCurrent(A)95V oltage(V)23Travel speed(mm/min)203Number of layers3Interpass temperature(◦C)94Heat Input(kJ/mm)0.7Fig.2.Schematic diagram for Ferrite Number determination.Table1Chemical composition of weld depositsC Mn Si P S Cr Ni Mo Al Ti Co V Cu Nb N C308H0.048 1.680.490.0290.00819.789.490.160.010.010.130.0860.230.010.82 M308H0.074 1.170.410.0340.01118.3910.510.170.0040.010.0300.0800.240.010.12 C316H0.065 1.700.400.0250.00719.1011.90 2.30––––0.200.010.03 M316H0.065 1.230.430.0380.01117.4013.47 2.22––––0.150.010.13286Y.Cui,C.D.Lundin /Materials Science and EngineeringA 452–453 (2007) 284–291Fig.3.Weldment preparation and schematic drawing of creep sample.The bend ﬁxture was used to perform the Fissure Bend Test on weld coupons to determine the microﬁssure distribution.The milled and surface ground weld pads were bent in tension to an angle of 120◦for detecting the microﬁssures present across the center 100mm of the pad surface for evaluation of microﬁssur-ing tendency.The number of microﬁssures was counted under the microscope at 100magniﬁcation.An average microﬁssure density of 7.9and 5.9cm −2was determined for modiﬁed E308H and E316H pads,meanwhile no microﬁssures were present in the commercial E308H and E316H weld pads.2.2.Creep property evaluation2.2.1.Sample preparationBefore welding,the plates were clamped on each side to a heavy backing ﬁxture to prevent excessive distortion.All weld-ing was accomplished with the same welding conditions as those for the electrode evaluation.Fig.3shows the groove joint prepa-ration,the application of two butter layers and the sequence of the joint.All weld-metal test specimens for creep testing were extracted along the longitudinal direction from the coupon.2.2.2.Creep testingThe creep testing was conducted in constant load creep frames.Each frame contains a three-zone furnace with the power level for each zone being independently adjustable.Each furnace is controlled by a Leeds and Northrup Electromax III controller which utilizes a chromel–alumel thermocouple to monitor the temperature at the center of the middle zone.Each specimen is mounted in a testing ﬁxture and suspended within the creep frame furnace.A chromel–alumel thermocouple wired to the center of the specimen gauge length is connected to a digi-tal temperature recorder which,in turn,is used to monitor the temperature of the specimen during testing.To minimize the convection of air through the furnace,both the top and bottomoriﬁces of the furnace were packed with ceramic wool.At the beginning of each test,the specimens are heated to the desired temperature and stabilized before any load is applied.Loading is in uniaxial tension with a constant load throughout the test.In addition to temperature,specimen extension,measured by a dial gauge attached to the testing ﬁxture,is also recorded as a function of time.Different stress levels between 70and 240MPa were used together with a range of temperature (550–700◦C)for creep testing of commercial and modiﬁed E308H and E316H weld deposits.3.Results and discussion 3.1.Creep testing resultsFig.4illustrates typical creep curves (strain versus time to rupture)for ﬁssure-containing and ﬁssure-free E316HsamplesFig.4.Typical creep curves (strain vs.time to rupture)for ﬁssure-containing and ﬁssure-free 316H samples under the same testing condition,117MPa and 660◦C.Y.Cui,C.D.Lundin/Materials Science and Engineering A 452–453 (2007) 284–291287Fig.5.(a).Creep-rupture behavior for E308H welds;(b)creep-rupture behavior for E316H welds;(c)creep-rupture behavior for commercial E308H and E316H.under the same testing conditions,117MPa and660◦C.Both curves match well up to1700h,then theﬁssure-containing spec-imen exhibits more secondary creep.The creep rate increases rapidly in the tertiary region that starts at approximately2% creep strain in both specimens.However,the time to rupture for ﬁssure-containing modiﬁed316H is1000h greater than com-mercial316Hﬁssure-free sample.The analysis of creep test results was conducted using the Larson–Miller Parameter technique as shown in Fig.5(stress level versus LMP).It is apparent that the creep properties of modiﬁed E316H(microﬁssure-containing)are superior to the commercial E316H(microﬁssure-free)samples;meanwhile modiﬁed E308H(ﬁssure-containing)sample shows lower creep properties than commercial E308H(ﬁssure-free)sample.3.2.Metallurgical evaluationSamples for microstructure evaluation were extracted from fractured creep specimens and ground and polished to0.05␮m surfaceﬁnish and electrolytically etched with potassium hydrox-ide to reveal the morphology of the microstructure.The etchant selection is considered to be sensitive in revealing sigma phase (colored)in austenitic stainless steel weld metals which have experienced long-term service at elevated temperature.The most successful etchant for revealing sigma phase is an electrolytic etchant containing potassium hydroxide(KOH–H2O)solution under a controlled(DC)current density and the etchant time.The solution preferentially etches sigma(relative to the austenitic grain boundaries)the color of which varies from yellow to reddish-brown under the optical microscope.Such characteristic colors and contrast made sigma phase identiﬁcation[19].Fig.6shows the microstructural morphologies of modiﬁed 308H samples before and after creep testing.Before and after creep testing,the microstructure of modiﬁed308H is austenite (FN=0),as shown in Fig.6(a).For commercial308H,the as-deposited microstructures are austenite with ferrite,austenite with ferrite and sigma after creep testing as shown in Fig.6(b).Fig.6(c)shows the microstructure of modiﬁed316H.Before creep testing,the microstructure is all austenite(FN=0).Dur-ing testing,carbides evolved in the vicinity of the substructure and grain boundaries.For commercial316H(FN=4.7),the microstructure is austenite with ferrite before creep testing and austenite with ferrite and sigma(deduced from morphology and color etching)after creep testing,as shown in Fig.6(d).288Y.Cui,C.D.Lundin /Materials Science and EngineeringA 452–453 (2007) 284–291Fig.6.Microstructure of samples before and after creep testing.(a)Modiﬁed E308H (138MPa,620◦C,746h);(b)commercial E308H (138MPa,645◦C,754h);(c)modiﬁed E316H (117MPa,660◦C,3671h);(d)commercial E316H (117MPa,660◦C,2685h).The sigma phase is distributed along the substructure and grain boundaries and shows reddish-brown under the microscope.SEM microstructural morphology of commercial and modi-ﬁed E316H samples after creep testing is presented in Fig.7as a back scattered image.The typical microstructure includes the coarse irregular-shaped secondary phase like the “islands”in the matrix in Fig.7(a)and the dark globular particles in Fig.7(b).The majority of the globular particles form,in modiﬁed E316H,along the substructure and grain boundaries and exhibit a size in the range of 0.2–0.4␮m while the size of the particles within the matrix is around 0.6␮m.EDS analysis was performed at location A for the irregular-shaped secondary phase and location B for matrix.The EDS spectra presented in Fig.8for locations A and B,respectively.The EDS results show that the irregular-shaped secondary phase contains higher Cr as compared to the matrix.In addition,the fact that these irregular-shaped secondary phasesY.Cui,C.D.Lundin /Materials Science and Engineering A 452–453 (2007) 284–291289Fig.7.SEM microstructural morphology of creep samples after testing (117MPa,660◦C),as a back scattered image (a)commercial E316H (2686h);(b)modiﬁed E316H (3671h).were stained red by potassium hydroxide etching,indicates that these are ␴phase.Aluminum oxide presented shown in Fig.8(a)(Al and O peaks)was involved from the polishing process with alumina powder.This can be deduced from the chemicalcom-Fig.8.The EDS spectra for locations A (a)and B (b)in Fig.7(a).position (less aluminum content)and further proved by the latter X-ray diffraction pattern (no aluminum peak appears again).The EDS spectra for particles and matrix for modiﬁed E316H do not indicate large difference in chemical composition because it is hard to isolate the small particles from the matrix using EDS.3.3.X-ray diffractionTo further verify the presence of sigma phase and precipita-tion,an X-ray diffraction apparatus was employed to carry out the analysis.An electrolytic precipitate exaction technique was used to obtain the precipitates from commercial and modiﬁed E308H and E316H samples before and after creep testing.To extract particles,a known weight of a sample was placed into 10%HCl +90%methanol solution with a constant voltage of 8V referred to the platinum electrode.A centrifuge was used to separate the particles from the solution.The particles collected from the solution were cleaned using high purity methanol.Then the particles were ready for X-ray diffraction.The par-ticles extracted are weighed again and the ratio of the weight percentage of the precipitate to the matrix is obtained from the following formula [20].The results of electrolytic extraction of particles from weld deposits are shown in Table 3.R = M r(M i f )×100,where M i is the initial mass of sample,M f the ﬁnal mass of sample after extraction and cleaning,M r the mass of residue and R is the residue,mass %.The X-ray diffraction (XRD)spectra were obtained in a Philips X’pert Pro Diffractometer at 45kV and 40mA.Diffrac-290Y.Cui,C.D.Lundin /Materials Science and Engineering A 452–453 (2007) 284–291Table 3Results of electrolytic extraction of particles from weld deposits Material M i (g)M f (g)M r (g)R (%)M316H bf 10.1990 5.47980.01140.242M316H af 0.57600.11140.0050 1.076C316H bf 19.946713.41840.03830.587C316H af 2.10040.27890.0360 1.976M308H bf 3.7304 2.37090.00400.294M308H af 1.96110.13190.0200 1.093C308H bf 4.7813 1.33510.00270.078C308H af1.88590.16950.00930.542tion patterns are acquired from samples in a step mode with 0.02◦step (2θ)and 4s per point over diffraction angles from 30◦to 60◦.The information from X-ray examination was recorded in the form of intensity as function of 2θ.It is evident that Cr 23C 6is the dominant precipitate with a few MnS inclusions for both commercial and modiﬁed 308H and 316H before creep testing.After creep testing most particles are Cr 23C 6and an amount of ␴-FeCr was observed in the commercial 316H sample.This agrees with the metallographic examination on this sample.The majority particles for modiﬁed and commercial 308H as well as modiﬁed 316H are Cr 23C 6.No ␴-FeCr was found in commer-cial E308H samples due to an insufﬁcient amount particles to be detected using X-ray diffraction.The typical X-ray spectra of modiﬁed and commercial 316H after creep testing are shown in Fig.9.Fig.9.Typical X-ray diffraction patterns obtained from modiﬁed and commer-cial E316H weld deposits after creep testing.3.4.Mechanism analysisAccording to the results on particles extracted from weld deposits of modiﬁed E308H and E316H (FN =0),the ratio of extracted particle weight (the ratio of the particle weight to the weight dissolved in electrolytic precipitate extraction)for these two deposits pre-and post-creep testing are in the same level,around 0.2and 1%,respectively.The precipitate ratio after creep testing is much greater than that before,which means that a sig-niﬁcant of carbides evolved after creep testing.The carbides in modiﬁed E316H are distributed in chains and those in modi-ﬁed E308H are distributed at random.For commercial E308H and E316H,the extraction ratios are quite different.Because of molybdenum added in E316H,more carbides formed in weld deposits for E316H than E308H before creep testing.After creep testing,more sigma phase formed in E316H than E308H which results in the large difference in extraction ratio for both of these commercial weld deposits.It is to be noted that microﬁssures decrease creep resis-tance for E308H because of the propagation paths provided by ﬁssures and the reduced beneﬁt effect of the randomly dis-tributed carbides.However,for commercial E316H,sigma phase formed along the grain boundaries due to the higher ferrite and Mo content (the extent of sigmatizion is greater than for commercial 308H).Since the sigma phase is hard and brittle it promotes secondary cracking between the sigma phase and austenite in the matrix under the stress.For modiﬁed E316H (ﬁssure-containing),carbides are distributed in a chain of dis-crete globular M 23C 6at the substructure and grain boundaries.This morphology beneﬁts creep-rupture life.The mechanisms causing creep are complex and not fully understood,but dislocation climb is thought to be important.To observe the morphology related to carbides and disloca-tion,a Hitachi 800H type transmission electron microscope was employed.The sample for TEM evaluation extracted from the transverse section of modiﬁed E316H sample after creep test,at 45◦along the loading axis.The chemical thinning was per-formed by using a type Tenupo-3dual electrolytic polishing equipment with a solution of 5%perchloric acid in methanol.Fig.10shows the typical TEM microstructural morphology of modiﬁed E316H after creep testing under 70MPa,700◦C and 4560h.From the metallurgraphy evaluation and particle extraction ratio,the concentration of the evolved carbides in the modiﬁed E316creep sample is high.At such high con-centrations,the precipitates may interact with the dislocation cooperatively rather than individually.Dislocations are multi-plied and locked by the ﬁne precipitate formed in austenite.It is evident that bonding of dislocation to the precipitates will be much stronger than it would be to an “atmosphere”.The precip-itates nucleated at dislocations most effectively retard slip.With increasing plastic deformation,the intersection of dislocations with each other grows to form a network as a forest of disloca-tions.Because of the particles in the forest,any slip dislocation does not travel far before it intersects other dislocations passing through its slip plane at various angles.The particles make the movement of the entangled dislocations through the lattice more difﬁcult.When part of the dislocation in the forest is locked,it isY.Cui,C.D.Lundin/Materials Science and Engineering A 452–453 (2007) 284–291291Fig.10.Typical TEM microstructural morphology of modiﬁed E316H after creep testing under70MPa,700◦C and4560h.hard to move entire network.This results in the density of dislo-cations on one side of a particle wall higher than the other side. It is not quite understood that why carbides distributed in a chain of discrete globular precipitates in the E316H weld metal,but in a random order in E308H weld deposits when both FNs are pared to the effect of microﬁssures and sigma phase in E316H and E308H weld deposits,it is concluded that secondary cracking caused by sigma phase is a main factor in effecting creep properties for E316H deposits,and the microﬁssures to E308H deposits.4.Conclusions1.The creep test results revealed that modiﬁed E316H with0FN(ﬁssure-containing deposits)have superior creep resistance, followed by commercial E316H and E308H,the modiﬁed 308H with0FN(ﬁssure-containing)samples showed the poorest performance.2.M23C6carbides evolved from modiﬁed E308H and E316Hweld coupons after creep testing when their Ferrite Numbers are0in as-welded samples.The majority of the carbides in modiﬁed316H(FN=0)in the range of0.2–0.4␮m dis-tributed in a chain of discrete globular M23C6along the substructure and grain boundaries while the carbides in mod-iﬁed E308H weld coupons(FN=0)are distributed in a random order.3.Sigma phase can be detected in commercial E316H andE308H samples after the creep tests.More sigma phaseformed in commercial E316H weld deposits than commercial E308H because of the difference in molybdenum content.4.Carbides evolved in a chain effectively retard the movementof dislocation which results in the higher creep properties of modiﬁed E316Hﬁssure-containing sample thanﬁssure-free.Fissure-containing modiﬁed E308H has a lower creep strength thanﬁssure-free commercial sample because of the propagation paths provided byﬁssures and the reduced effect on the randomly distributed carbides.5.Creep strength of austenitic stainless weld metals is as a func-tion of ferrite:secondary cracking caused by sigma phase (high ferrite content)is a main factor in effecting creep prop-erties for E316H deposits,and the microﬁssures to E308H deposits(low ferrite content).AcknowledgementsThe author acknowledges theﬁnancial support from the Welding Research Council.The authors are grateful to Dr.D.J. Kotecki(The Lincoln Electric Co.)and Mr.Frank Lake(ESAB) for supplying the electrodes.References[1]J.R.Davis,Stainless Steels,ASM Specialty Handbook,ASM International,1996.[2]J.C.Borland,R.N.Younger,Br.Weld.J.8(1960)22–59.[3]R.G.Bake,Br.Weld.J.15(1968)283–295.[4]R.G.Baker,R.P.Newman,Met.Construct.Br.Weld.J.1(1969)1–4.[5]A.M.Rirrer,W.F.Savage,Metall.Trans.A17A(1986)727–737.[6]H.Thielsch,Weld.Eng.52(1967)80–85.[7]T.G.Gooch,J.Honeycomb,Met.Construct.9(1970)375–380.[8]C.D.Lundin,D.F.Spond,Weld.J.55(1976)356s–366s.[9]C.D.Lundin,Weld.J.8(1980)226s–232s.[10]R.Nakkalil,N.L.Richards,M.C.Chaturvedi,Metall.Trans.A24A(1993)1169–1179.[11]C.D.Lundin,C.P.D.Chou,Weld.J.64(1985)113s–118s.[12]F.C.Hull,Weld.J.46(1967)339s–409s.[13]C.D.Lundin,W.T.DeLong,D.F.Spond,Weld.J.54(1975)241s–246s.[14]A.L.Schaefﬂer,Met.Prog.56(1949)680–680B.[15]W.T.DeLog,Weld.J.53(1974)273s–286s.[16]D.J.Kotecki,T.A.Siewert,Weld.J.71(1992)171s–178s.[17]J.M.Vitek,S.A.David,C.R.Hinman,Weld.J.82(2003)10s–17s,and43s–50s.[18]C.D.Lundin,W.T.DeLong,D.F.Spond,Weld.J.55(1976)145s–151s.[19]L.Patel,The effect of carbon on the formation of sigma phase inaustenitic stainless steel,Master Thesis,The University of Tennessee,1981, p.81.[20]ASTM Designation:E963-95,Standard Practice for Electrolytic Extractionof Phase from Ni and Ni–Fe Base Superalloys Using a Hydrochloric-Mehanol Electrolyte.。

Scheme-invariant NNLO evolution for unpolarized DIS structure functions

a r X i v :h e p -p h /0411110v 1 8 N o v 2004DESY 04-218hep-ph/0411110October 2004SFB/CPP-04-060Scheme-invariant NNLO evolution for unpolarized DIS structure functionsJ.Bl¨u mlein a and A.Guﬀanti aaDESY,Platanenallee 6,D–15738Zeuthen,GermanyWe discuss the combination of NNLO standard QCD evolution and scheme-invariant analysis for unpolarized DISstructure functions data as a method to reduce the theoretical errors on the determination of αs (M 2Z )to ∼1%in order to match the accuracy forseen for experimental errors from future high statistics measurements.1.INTRODUCTIONThe ﬁnal HERA-II data on unpolarized deeply in-elastic scattering (DIS)structure functions,com-bined with the present world data,will allow to reduce the experimental error on the strong cou-pling constant,αs (M 2Z ),to the level of 1%[1].On the theoretical side,the next-to-leading order (NLO)analyses have intrinsic limitations which allow no better than 5%accuracy in the deter-mination of αs [2].In order to match the ex-pected experimental accuracy,analyses of DIS structure functions need then to be carried out at the NNLO level,which requires the knowledge of the β–function and anomalous dimensions at the 3-loop level and the massless and massive 2-loop Wilson coeﬃcients.With the recent com-putation of the 3–loop anomalous dimensions [3],the whole scheme independent set of quantities is known,thus allowing a complete NNLO study of DIS structure functions.At the same time we think that combining the standard QCD analysis and ﬁts based on scheme-invariant evolution will provide a valuable tool to reduce theoretical and conceptual uncertainties in high-precision analy-ses aiming at 1%accuracy.Our ﬁnal goal is to perform the full NNLO anal-ysis of DIS structure functions aiming at an high-accuracy determination of αs and the extraction of a set of parton distribution functions (PDFs)with fully correlated errors.A complete analysisrefers to both the singlet and non-singlet evolu-tion.In the present letter we will concentrate only on the singlet sector,referring the reader to the recent non-singlet analysis [4].2.QCD EVOLUTION EQUATIONS Evolution equations of DIS structure functions depend,in the standard QCD approach,on two arbitrary scales which are introduced in the calcu-lation:the renormalization and the factorization scales.The renormalization scale dependence of any observable can be removed only summing the per-turbative series to all orders.Its presence is then unavoidable in any ﬁxed order result.Moreover,the dependence of the result on the variation of this unphysical scale can be used to give a rough estimate of the theoretical error due to higher or-der corrections.On the other hand,if we consider the depen-dence of the result on the factorization scale we may follow two approaches.The ﬁrst one is to consider the evolution of parton distribution func-tions which are process-independent but depend on the adopted factorization scheme.The sec-ond one is to study evolution equations for phys-ical observables.In these equations the rˆo le of anomalous dimensions for mass factorization is played by physical anomalous dimensions,which are independent of the factorization scheme but12depend on the process and the observables con-sidered.These two choices deﬁne what we call the standard QCD analysis and the scheme-invariant analysis.In the standard QCD analysis one introduces a parameterization for the diﬀerent PDFs at a given reference scale.The PDFs are then evolved up to the actual scale of the process,solving the evolution equations for mass factorization.Struc-ture functions are then constructed as a convolu-tion of the PDFs and the corresponding Wilson coeﬃcients.As a last step,a multi-parameter ﬁt is then performed to extract the value of the coupling constant and determine the parameters entering the PDF parameterization.In a scheme-invariant analysis the parameter-ization of the observable at the reference scale Q20is extracted from the data.The value of the observable at the scale Q2is determined solving the evolution equations with physical anomalous dimensions as evolution kernels.Finally a one-parameterﬁt is performed to extract the value ofαs(M2Z).Once the analysis is completed the parton densities in any factorization scheme can be extracted along with the respective experimen-tal errors.The advantage of considering factor-ization scheme invariant evolution equations for physical observables resides in the fact that the input distributions are observables.Full exploita-tion of this advantage requires therefore high statistics measurements to minimize errors on the input distributions.Furthermore,the correla-tions between the measured input distributions have to be considered in detail.Once more we would like to stress that the two analyses are complementary and not mutually ex-clusive.Thus performing both of them and com-paring the extracted values ofαs(M2Z),or corre-spondinglyΛQCD,provides a test of stability to determine the QCD parameter.3.PHYSICAL ANOMALOUS DIMEN-SIONSWhen considering the singlet evolution the quark-singlet and gluon PDFs can be mapped into a pair of structure functions via the matrix of Wilson coeﬃcients,C N,[5]:F N A F N B = C N A,ΣC N A,gC N B,ΣC N B,gΣN G N .(1)In Eq.(1),as we will do in the following,we work in Mellin space,where convolutions are ordinary products.The singlet evolution equations readd4K N F N A F N B ,(2) where the evolution variable ist=−2a s(Q20).(3)The coupling constant a s is related to the usual strong interactions coupling via the relationa s(µ2)=αs(µ2)β0L 1−β1ln Lβ40L2 , whereL=lnQ2dµ2=−∞n=0βn a n+2s(µ2)(7)and,in the case of SU(3)c,the coeﬃcients enter-ing up to3-loops areβ0=11−23N f,(8)β2=285718N f+3253 terms of the anomalous dimensions and the Wil-son coeﬃcients as[5]K N IJ= −4∂C N I,m(t)2β(a s(Q2))C N I,m(t)γN mn(t) C N −1n,J(t) .HereγN mn denotes the unpolarized anomalous di-mensions which are related to the evolution ker-nels in x−space byγN mn=−2 10dx x N−1P mn(x),m,n=q,g(10)and C N I,m are the Mellin transforms of the WilsoncoeﬃcientsC N I,m= 10dx x N−1C I,m(x).(11)While the anomalous dimensions and the Wilsoncoeﬃcients are,separately,factorization-schemedependent quantities,the combinations(9)deﬁn-ing the physical anomalous dimensions are fac-torization scheme invariants,order by order inperturbation theory.Diﬀerent pairs of structure function can betaken into consideration,in particular:•F2and∂F2/∂t[6,5,7];•F2and F L[8,5].In the case of polarized DIS a combined4 γN(0)qqγN(0)gg−γN(0)qgγN(0)gq ,K N(0)dd =γN(0)qq+γN(0)gg.NLO:K N(1)22=K N(1)2d=0(13)K N(1)d2=12β0 γN(0)qqγN(0)gg−γN(0)gqγN(0)qg+β02C N(1)2,g2 γN(1)qq−γN(0)qqγN(1)qgβ0 γN(0)qq+γN(0)gg−2β04 γN(2)qqγN(0)gg+γN(0)qqγN(2)gg−γN(2)qgγN(0)gq−γN(0)qgγN(2)gq+γN(1)qqγN(1)gg−γN(1)qgγN(1)gq+β04+β203C N (1)2,q2−4C N (2)2,q+β12β0γN (1)qq γN (0)gg +γN (0)qq γN (1)gg−γN (1)qg γN (0)gq −γN (0)qg γN (1)gq+3β2γN (0)qq γN (0)gg −γN (0)qg γN (0)gq−β2γN (0)qg2β30C N (1)2,q C N (1)2,g+β1C N (1)2,g+C N (1)2,gγN (1)qq+C N (1)2,g γN (0)gq+β0C N (1)2,g C N (1)2,q γN (0)qqγN (0)qq −γN (0)gg+γN (0)qqC N (1)2,g γN (1)gg+C N (2)2,g γN (0)gg+β02γN (0)qq γN (1)qq+γN (1)qq γN (1)gq+C N (1)2,g2γN (0)gqγN (0)gg −3γN (0)qg2−β20C N (1)2,g2γN (0)qq+β0−C N (1)2,g γN (0)qqγN (1)qg +C N (1)2,g2γN (0)qqγN (0)qq −γN (0)gg+γN (0)qqγN (0)gg2C N (1)2,g2γN (0)qq γN (0)qq −γN (0)gg2−γN (0)qqγN (1)qg2+C N (1)2,g γN (1)qgγN (0)qqγN (0)qq−γN (0)ggK N (2)dd=γN (2)qq +γN (2)gg −4β2−4β0C N (1)2,q2−2C N (2)2,q+β21β0γN (0)qq +γN (0)gg−β1γN (0)qg4β0C N (2)2,g−C N (1)2,q C N (1)2,g+γN (0)qq −γN (0)ggC N (1)2,g C N (1)2,q−C N (2)2,g−C N (1)2,gγN (1)qq −γN (1)gg −2β1−C N (1)2,g2γN (0)gq +γN (2)qg+2β050.511.522.5310101010F 2 S (x )Figure 1.NLO scheme invariant evolution for the singlet part of the structure function F 2for four light ﬂavors.structure function F 2which,depending on actual event kinematics,can receive contributions from heavy ﬂavors up to the level of 20−40%.Any analysis aiming at extracting αs form DIS struc-ture functions data with an accuracy of ∼1%must,therefore,take into account heavy ﬂavor contributions.Recently a parameterization of heavy ﬂavor Wilson coeﬃcients in Mellin space has been derived [11],thus allowing a direct in-corporation into computer codes which solve the evolution equation in Mellin space.5.NUMERICAL RESULTSWhile full numerical implementation of the NNLO scheme invariant evolution is almost ﬁn-ished,as a preliminary result,in Fig.1and Fig.2we present the scheme invariant evolution for the structure functions F 2and ∂F 2/∂t at NLO for four light ﬂavors.In the present computation the initial form of the observables is built up as a convolution of Wilson coeﬃcients and PDFs atthe reference scale Q 20=1GeV 2,using parame-terization of [12].-2.52.557.51012.51517.52010101010xd F 2 S/d t (x )Figure 2.NLO scheme invariant evolution for the singlet part of ∂F 2/∂t for four light ﬂavors.6.CONCLUSIONSThe future high precision HERA-II data will al-low a reduction of the experimental error on the determination of αs to ∼1%.On the theoret-ical side,the inclusion of NNLO corrections is mandatory to cope with such a level of accu-racy.In view of a high accuracy determination of the strong coupling constant we think that com-bining the standard6Neerven,Nucl.Phys.B586(2000)349.6.W.Furmanski and R.Petronzio,Z.Phys.C11(1982)293.7.J.Bl¨u mlein and H.B¨o ttcher,Nucl.Phys.B636(2002)225.8.S.Catani,Z.Phys.C75(1997)665.9.L.Baulieu and C.Kounnas,Nucl.Phys.B155(1979)429.10.J.Bl¨u mlein and S.Kurth,Phys.Rev.D69(1999)014018;J.Bl¨u mlein,mun.133 (2000)76;159(2004)19.11.S.I.Alekhin and J.Bl¨u mlein,Phys.Lett.B594(2004)299.12.A.D.Martin,R.G.Roberts,W.J.Stirlingand R.S.Thorne,Eur.Phys.J.C23(2002) 73。

非保守荷载超弹性大变形分析的复变量无单元Galerkin方法

摘要不同于其它数值计算方法在求解过程中需要划分网格，无网格法在求解力学问题时只需要定义节点，直接建立系统代数方程，在涉及网格畸变、网格移动等问题时具有灵活性、自适应性，是一种具有强大发展潜力的数值计算方法。

无单元Galerkin方法是目前应用最广的无网格计算方法，本文将复变量移动最小二乘近似引入无单元Galerkin方法中，可以改进无单元Galerkin方法中计算量大的问题。

相对于移动最小二乘近似，采用复变量移动最小二乘近似中基函数的维数降低，从而试函数中的系数项减少，问题域中需要的节点数也相应减少，计算效率提高。

在实际工程结构和材料的大变形过程中，外荷载往往会随着受力面的变形而发生变化，此时荷载是依赖于变形状态的非保守力，数值处理相对复杂。

相较于弹性材料的大变形分析，超弹性材料在受力作用下可以产生更大的变形，而且由于其近不可压性，在采用数值方法进行求解时易出现体积锁死和压力震荡现象，造成分析困难。

综上所述，有必要研究非保守荷载下超弹性材料的大变形问题。

使用有限元方法解决这类问题时易发生网格畸变，无网格法由于其自身的优越性，在处理这类问题上有很大的优势。

本文将复变量无单元Galerkin方法应用于求解非保守荷载下弹性和超弹性大变形问题，采用罚函数法引入本质边界条件，推导了非保守荷载大变形问题的增量形式的完全Lagrange格式的Galerkin积分弱形式。

采用混合变量法解决超弹性材料的不可压性带来的求解困难，采用复变量移动最小二乘法建立位移场的逼近函数，推导了相应的超弹性切线模量、应变位移转换矩阵和刚度矩阵，建立了无网格大变形分析的离散方程，采用Newton-Raphson法进行迭代求解。

本文建立了非保守荷载作用下超弹性大变形分析的算法流程，编制了MATLAB计算程序，对经典悬臂梁算例、蜂窝结构以及纯弯梁算例等进行了计算分析。

与无单元Galerkin方法得到的结果相比，采用复变量无单元Galerkin 方法计算效率更高；采用复变量无单元Galerkin方法分析大转动问题时能得到非常大的变形而不会因产生网格畸变导致很大的误差；对三维超弹性材料进行模拟与分析，分析了超弹性材料在基本荷载作用下的应力应变关系；分析了采用复变量无单元Galerkin方法求解负泊松比结构的可行性，为研究负泊松比结构的物理特性和力学性能奠定了基础。

语言学名词解释合集

英语语言学名词解释Synchronic: said of an approach that studies language at a theoretical “point”in time. Diachronic: said of the study of development of language and languages over time.Arbitrariness: the absence of any physical correspondence between linguistic signals and the entities to which they refer. Duality: the structural organization of language into two abstract levels; meaningful units and meaningless segments .Competence: unconscious knowledge of the system of grammatical rules in a language. Performance: the language actually used by people in speaking or writing. Langue: the language system shared by a “speech community”.Parole: the concrete utterances of speaker.Morpheme: the smallest unit of language in terms of the relationship between expression and content, a unit that cannot be divided into further smaller units without destroying or drastically altering the meaning, whether it is lexical or grammatical.Inflection: is the manifestation of grammatical relationship through the addition of inflectional affixes such as number, person, finiteness, aspect and cases to which they are attached.Root: refers to the base form of a word that cannot be further analyzedwithout loss of identity. Stem:is any morpheme or combinations of morphemes to which an inflectional affix can be added.Acronym:is made up from the first letters of the name of an organization,which has a heavily modified headword.Syntax: the study of the interrelationships between elements in sentence structure.Subordination: the process or result of linking linguistic units so that they have different syntactic status, one being dependent upon the other, and usually a constituent of the other. Denotation: denotation involves the relationship between a linguistic unit and the non-linguistic entities to which it refers.Connotation: properties of the entity a word denote.Synonymy: synonymy is the technical name for one of the sense relations between linguistic units, namely the sameness relation.Hyponymy: the technical name for inclusiveness sense relation, is a matter of class membership.Entailment: This a logic relationship between two sentences in which the truth of the second necessarily follows from the truth of the first, while the falsity of the first follows from the falsity of the second. Traffic light does not have duality. Obviously, it is not a double-level system. There is only one-to-one relationship between signs and meaning but the meaning units cannot be divided into smaller meaningless elementsfurther. So the traffic light only has the primary level and lacks the secondary level like animals’call.Critical Period Hypothesis The critical period for language acquisition 语言获得的关键期Eric Lenneberg was a major proponent.The critical period hypothesis关键期假设It refers to a period in one’s life extending from about age two to puberty, during which the human brain is most ready to acquire a particular language and language learning can proceed easily, swiftly, and without explicit instruction. It coincides with the process of brain lateralization. Prior to this period, both hemispheres are involved to some extent in language and one can take over if the other is damaged .「语言学习关键期」（the critical period）的争议。

细胞结构英文版27张幻灯片

Needed to continue glucose breakdown for energy
NAD+
cytoplasm
fermentation
Electron carrier produced in glycolysis
fermentation lactate
when oxygen is available
Contains digestive enzymes to digest food in protists or destroy aging organelles
Endomembrane System
Rough Endoplasmic
Reticulum
Smooth Endoplasmic
Reticulum
Structure
Cilia and Flagella
Function(s)
• Move substances across cell surface in lungs, fallopian tubes
• Cell movement in sperm
Connections Between Cells
Citric acid cycle
Electron Transport chain
oxygen Outside cell
mitochondrion
2 ATP
2 ATP
32 ATP
Energy Yield from Glucose
Without Oxygen, Fermentation Occurs
Structure
Mitochondrion
Function
Captures energy from organic molecules, producing ATP

Hadron Structure Functions in a Chiral Quark Model

iD iD5 = = i∂ / − (S + iγ5 P ) + Qv / =: iD(π) + Qv / −i∂ / − (S − iγ5 P ) − Qv / =:
(π ) iDRON STRUCTURE FUNCTIONS IN A CHIRAL QUARK MODEL Leonard Gamberg∗ )
Department of Physics and Astronomy, University of Oklahoma, 440 West Brooks, Norman, OK 73019
arXiv:hep-ph/9910503v1 27 Oct 1999
Herbert Weigel‡ )
Center for Theoretical Physics, Laboratory of Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139 OKHEP-99-06, MIT-CTP-2913 We present a consistent regularization procedure for calculating hadron structure functions in a bosonized chiral quark model. We ﬁnd that the Pauli–Villars regularization scheme is most suitable. We also summarize the phenomenology of structure functions calculated in the valence quark approximation.

Structural Studies of the Ferroelectric Phase Transition in Bi4Ti3O12

Structural Studies of the Ferroelectric Phase Transitionin Bi4Ti3O12Qingdi Zhou and Brendan J.Kennedy*School of Chemistry,The University of Sydney,Sydney,NSW2006AustraliaChristopher J.HowardAustralian Nuclear Science and Technology Organization,Private Mail Bag1,Menai, NSW2234,Australia,and School of Physics,The University of Sydney,Sydney,NSW2006AustraliaReceived July3,2003.Revised Manuscript Received October20,2003A variable-temperature synchrotron X-ray diffraction study of the phase transitions in the ferroelectric n)3Aurivillius oxide Bi4Ti3O12is described.At room temperature the structure of Bi4Ti3O12is orthorhombic in space group B2eb and this continuously transforms to the high-temperature tetragonal I4/mmm structure via an intermediate orthorhombic phase.The possible space groups of this intermediate orthorhombic phase have been identified by using group theory.IntroductionThe Aurivillius oxides are represented by the general formula(Bi2O2)2+(A n-1B n O3n+1)2-where B is a diamag-netic transition metal such as Ti4+or Nb5+and A is an alkali or alkaline earth cation.1The structure of the Aurivillius oxides consists of arrays of Bi2O2and per-ovskite-like A n-1B n O3n+1layers.The ferroelectric prop-erties of such oxides have been known for around50 years,2,3yet the structural origins of their ferroelectricity have only recently been established.4,5Following the pioneering work of Scott and co-work-ers,6the possibility of employing these Aurivillius oxides in ferroelectric memory devices has been extensively studied.A serious barrier to their practical utilization is their poor thermal stability.7-10Formation of thin-film ferroelectric devices involves a sintering step at high temperatures and this invariably degrades the performance of the simpler Aurivillius oxides.Conse-quently,a number of studies of the high-temperature behavior and structures of Aurivillius oxides have been reported.11-14In comparison to the n)2oxides based on SrBi2Ta2O9very little is known about the high-temperature properties of the n)3oxides such as Bi4-Ti3O12,yet such oxides are reported to have ferroelectric properties superior to those of the better-studied n)2 oxides.15Although it has been reported5that Bi4Ti3O12is monoclinic at room temperature,very-high-resolution powder diffraction data suggest that powder samples of Bi4Ti3O12are actually orthorhombic at room temper-ature.16Heating Bi4Ti3O12above670°C is reported to result in an apparently first-order phase transition to a paraelectric tetragonal phase.16,17A significant volume change between the high-temperature and low-temper-ature phases is likely to be detrimental to the stability of any thin films annealed or sintered above the Curie temperature.Conversely,continuous transitions are less likely to adversely influence the properties of the thin films.Hervoches and Lightfoot have demonstrated, using powder neutron diffraction methods,that for Bi4-Ti3O12the high-temperature paraelectric phase is in space group I4/mmm and that the room-temperature orthorhombic phase is in B2eb.16The main structural basis for the ferroelectricity in Bi4Ti3O12is the displacement of the Bi atoms within the perovskite-like layers,along the crystallographic a-axis with respect to the chains of corner-sharing TiO6 octahedra.This corresponds to a[110]displacement referred to the parent I4/mmm.The TiO6octahedra are tilted relative to each other and the tilt system can be*To whom correspondence should be addressed.Phone:61-2-9351-2742.Fax:61-2-9351-3329.E-mail: b.kennedy@.au.(1)Aurivillius,B.Arkiv Kemi1949,1,463.(2)Subbarao,E.C.J.Phys.Chem.Solids1962,23,665.(3)Smolenskii,G.A.;Isupov,V.A.;Agranovskaya,A.I.Sov.Phys. Solid State1961,3,651.(4)Rae,A.D.;Thompson,J.G.;Withers,R.Acta Crystallogr.,Sect. B:Struct.Sci.1992,48,418.(5)Rae,A.D.;Thompson,J.G.;Withers,R.;Willis,A.C.Acta Crystallogr.,Sect.B:Struct.Sci.1990,46,474.(6)Paz de Araujo,C.A.;Cuchlaro,J.D.;McMillan,L.D.;Scott, M.;Scott,J.F.Nature(London)1995,374,627.(7)Shimakawa,Y.;Kubo,Y.;Tauchi,Y.;Kamiyama,T.;Asano,H.; Izumi,F.Appl.Phys.Lett.2000,77,2749.(8)Shimakawa,Y.;Kubo,Y.;Tauchi,Y.;Asano,H.;Kamiyama,T.; Izumi,F.;Hiroi,Z.Appl.Phys.Lett.2001,79,2791.(9)Boulle, A.;Legrand, C.;Guinebretie`re,R.;Mercurio,J.P.; Dauger,A.Thin Solid Films2002,391,42.(10)Aizawa,K.;Tokumitsu,E.;Okamoto,K.;Ishiwara,H.Appl. Phys.Lett.2000,79,2791.(11)Macquart,R.;Kennedy,B.J.;Hunter,B.A.;Howard,C.J.; Shimakawa,Y.Integr.Ferroelectr.2002,44,101-112.(12)Hervoches,C.H.;Irvine,J.T.S.;Lightfoot,P.Phys.Rev.B 2002,64,100102(R).(13)Liu,J.;Zou,G.;Yang,H.;Cui,Q.Solid State Commun.1994, 90,365.(14)Macquart,R.;Kennedy,B.J.;Vogt,T.;Howard,C.J.Phys. Rev B2002,66,212102.(15)Park,B.H.;Kang,B.S.;Bu,S.D.;Noh,T.W.;Lee,J.;Jo,W. Nature(London)1999,401,682.(16)Hervoches,C.H.;Lightfoot,P.Chem.Mater.1999,11,3359.(17)Hirata,T.;Yokokawa,T.Solid State Commun.1997,104,673.5025Chem.Mater.2003,15,5025-502810.1021/cm034580l CCC:$25.00©2003American Chemical SocietyPublished on Web11/21/2003described as a-a-c0in Glazer’s notation.18These two structural features act in concert to lower the symmetry from tetragonal to orthorhombic,however,they are not linked,and there is no reason to suppose that both modes will condense at precisely the same temperature. Rather,it is probable that these modes will condense successively and the two end member phases will be linked by an intermediate ing powder neutron diffraction methods,Macquart and Lightfoot have in-dependently shown that the A21am to I4/mmm transi-tion in the n)2Aurivillius phases SrBi2Ta2O911and Sr0.85Bi2.1Ta2O912proceeds via an intermediate paraelec-tric Amam phase in each case.This Amam phase is also seen in PbBi2M2O9(M)Nb,Ta).19That is,upon cooling from the I4/mmm phase,the tilting of the octahedra occurs before the cation displacement.The same se-quence is reported to occur in the n)4Aurivillius oxide SrBi4Ti4O15.20The aim of the present work is to establish whether the B2eb to I4/mmm transition in Bi4Ti3O12is first order as proposed by Hirata and Yokakowa17or if it actually occurs continuously via an intermediate phase as seen in SrBi2Ta2O9.11To establish this we have investigated the temperature dependence of the structure of Bi4-Ti3O12from room temperature to800°C using high-resolution synchrotron radiation.Near the Curie tem-perature fine temperature intervals have been used to detect the intermediate phase which exists over a very limited temperature range.Experimental SectionThe crystalline sample of Bi4Ti3O12was prepared by the solid-state reaction of stoichiometric quantities of Bi2O3 (99.999%,Aldrich)and TiO2(99.9%,Aldrich).The heating sequence used was700°C/24h and850°C/48h,with intermediate regrinding.The sample was slowly cooled to room temperature in the furnace.The sample purity was established by powder X-ray dif-fraction measurements using Cu K R radiation on a Shimadzu D-6000Diffractometer.Room-and variable-temperature syn-chrotron X-ray powder diffraction patterns were collected on a high-resolution Debye Scherrer diffractometer at beamline 20B,the Australian National Beamline Facility,at the Photon Factory,Japan.21The sample was finely ground and loaded into a0.3-mm quartz capillary that was rotated during the measurements.All measurements were performed under vacuum to minimize air scatter.Data were recorded using two Fuji image plates.Each image plate was20×40cm and each covered40°in2θ.A thin strip(ca.0.5cm wide)was used to record each diffraction pattern so that up to30patterns could be recorded before reading the image plates.The data were collected at a wavelength of0.75Å(calibrated with a NIST Si 640c standard)over the2θrange of5-75°with step size of 0.01°.The patterns were collected in the temperature range of100-800°C in25°C steps or600-803°C in7°C steps, and with30-min counting time at each temperature.Struc-tures were refined by the Rietveld method using the program Rietica.22The positions of the cations were well described in these analyses,however the estimated standard deviations (esds)of the Ti-O bond distances(typically around0.02Å) preclude any detailed discussion of the temperature depen-dence of the bond distances.Results and DiscussionThe published room-temperature structure for Bi4-Ti3O12was used as a starting model in our Rietveldrefinements,and the structural refinement proceededwithout event.The temperature dependence of thelattice parameters and volumes are illustrated in Figure1.All the lattice parameters show a smooth increasedue to thermal expansion as the sample is heated toca.500°C.Above this temperature the cell continuesto expand along both the b-and c-directions,howeverthe a-parameter is essentially constant.This behavioris very similar to that displayed by a number of simplerABO3perovskites23-25and is apparently related to thegradual reduction in distortion resulting from a reduc-tion in the magnitude of the tilting of the BO6octahedraas the temperature is increased.Near675°C there is arapid decrease in the a-parameter although as is clearlyevident from Figure1this is not a discontinuousdecrease but rather a rapid progressive drop.At thesame temperature the c-axis expands rapidly,Figure1.The transition to the tetragonal phase is clearlyevident in the200/020and317/137reflections(near2θ≈15.8and26.7°,respectively,whereλ)0.75Å).As illustrated in Figure2the diffraction pattern recordedat670°C shows obvious splitting of the200/020and317/137reflections that is clearly indicative of orthor-hombic symmetry.This splitting remains clearly visibleto the eye until677°C and can be discerned by profileanalysis at684°C.At691°C no splitting or diagnosticasymmetry of these or other peaks is apparent and itis concluded that the structure is tetragonal.That is,the transition to the tetragonal structure occurs near690°C,which is around15°above the reported ferro-electric Curie temperature for Bi4Ti3O12.(Some care isrequired when comparing the transition temperaturesreported in various studies because of both samplevariation(induced by the different heating regimesused)and possible variations in the high-temperaturethermometry.)Above691°C the structure has been refined in thetetragonal space group I4/mmm and is as described byHervoches and Lightfoot.16That the paraelectric phaseis tetragonal in I4/mmm well above the ferroelectricCurie temperature was confirmed from the high-resolu-tion powder neutron diffraction data by Hervoches andLightfoot from both the cell metric and the absence ofany superlattice reflections indicative of TiO6tilting. The thermal expansion of the c-axis both above and below the T c is relatively linear and can be well-fitted to a simple linear equation c)5.277×10-4T+32.725 for T<677°C,and c)5.116×10-4T+32.725for T> 691°C.Examining the temperature dependence of the long c-axis we observed a large difference between the(18)Glazer,A.M.Acta Crystallogr.B1972,28,3384.(19)Macquart,R.;Kennedy,B.J.;Hunter,B.A.;Howard,C.J.J. Phys.:Condens.Matter2002,14,7955.(20)Hervoches,C.H.;Snedden,A.;Riggs,R.;Kilcoyne,S.H.; Manuel,P.;Lightfoot,P.J.Solid State Chem.2002,164,280.(21)Sabine,T.M.;Kennedy,B.J.;Garrett,R.F.;Foran,G.J.; Cookson,D.J.J.Appl.Crystallogr.1995,28,513.(22)Howard C.J.;Hunter,B.A.A Computer Program for Rietveld Analysis of X-ray and Neutron Powder Diffraction Patterns;Lucas Heights Research Laboratories:New South Wales,Australia,1998; pp1-27.(23)Howard,C.J.;Knight,K.S.;Kisi,E.H.;Kennedy,B.J.J. Phys.:Condens.Matter2000,12,L677.(24)Kennedy,B.J.;Howard,C.J.;Thorogood,G.J.;Hester,J.R. J.Solid State Chem.2001,161,106.(25)Kennedy,B.J.;Howard,C.J.;Chakoumakos,B.C.J.Phys. C:Condens.Matter1999,11,1479.5026Chem.Mater.,Vol.15,No.26,2003Zhou et al.values of the low-temperature orthorhombic,ferroelec-tric phase and those for the high-temperature tetragonal and paraelectric phase.Clearly the value for the c -parameter at 684°C does not fall into either series.A similar conclusion can be made for both the a -and b -parameters.These temperature-dependent changes in the lattice parameters are more reminiscent of the continuous-phase transitions observed in oxides such as Bi 2PbNb 2O 919than of the more subtle changes observed in the high-temperature second-order incommensurate-to-commensurate phase transition observed in Bi 2-MoO 6.26A feature of many first-order phase transitions is the coexistence of a two phase region.Attempts to fit the pattern at 684°C to a two-phase orthorhombic/tetragonal model with lattice parameters obtained by appropriate linear extrapolation were unsuccessful.It was concluded that a single phase was present at this temperature and this was neither the orthorhombic in B 2eb nor the tetragonal I 4/mmm .(26)Buttrey,D.J.;Vogt,T.;White,B.D.J.Solid State Chem.2000,155,206.(27)/∼stokesh/isotropy.html.Figure 1.Temperature dependence of the lattice parameters and volume for Bi 4Ti 3O 12obtained from Rietveld analysis of variable-temperature synchrotron diffraction data.For ease of comparison the values in the 2× 2×1orthorhombic cells have been reduced to the equivalent tetragonal values.Figure 2.Portions of the Rietveld fits for Bi 4Ti 3O 12showing the temperature dependence of the splitting of the tetragonal 110reflection into the orthorhombic 200/020pair near 2θ)15.8°and of the 127reflection into the 317/137pair near 2θ)26.8°.The 0012reflection is apparent near 2θ)15.6°.Ferroelectric Phase Transition in Bi 4Ti 3O 12Chem.Mater.,Vol.15,No.26,20035027In summary,we observe an orthorhombic structure at 684°C whose lattice parameter clearly distinguishes it from the low-temperature orthorhombic and high-temperature tetragonal phases.(In fact,even if we could not distinguish this as a separate phase,the observed continuity of transition,together with the group theo-retical arguments to follow,would indicate that such an intermediate orthorhombic phase is involved in the transition.)If we assume that all three phases have commensurate structures then it should be possible to identify the space group of the intermediate phase from a group theoretical analysis.To do this we used the program ISOTROPY.27This analysis confirmed that a direct B 2eb to I 4/mmm transition could not be continu-ous.The two modes responsible for the transition were identified as Γ5-describing the cation displacement and X 3+associated with the tilting of the TiO 6octahedra.28Whichever of these modes condenses first,an interme-diate orthorhombic structure based on a 2× 2×1superstructure of the parent I 4/mmm structure is involved,as illustrated in Figure 3,and the successive phase transitions through either of these intermediates are allowed to be continuous.If the initial distortion is cation displacement via the Γ5-mode then a ferroelec-tric orthorhombic structure that lacks any tilting of the TiO 6octahedra is expected.The resulting structure in Fmm 2can continuously transform to the observed room-temperature orthorhombic B 2eb phase through tilting of the TiO 6octahedra via the X 3+mode.(This descrip-tion refers still to the parent structure in I 4/mmm .)Alternatively,the initial distortion may be the introduc-tion of tilting of the TiO 6octahedra resulting in a Cmca phase followed by cation displacement.The available synchrotron diffraction data do not allow us to unequivoc-ally distinguish between these two possibilities;how-ever,by analogy with SrBi 2Ta 2O 9,we favor the latter possibility.11The confirmation of this will require a high-resolution neutron diffraction study.It is illuminating to compare our results with those of Hirata and Yokokawa.17First,Figure 2of their report suggests they recorded very little data in the ferroelec-tric phase with only four temperature points obvious.A somewhat greater number of temperatures were examined (nine)in the paraelectric phase,apparently at 20°C intervals.Crucially,no data appear to have been collected between 475and 675°C,the latter corresponding to the reported ferroelectric Curie tem-perature for Bi 4Ti 3O 12.There is then a relatively large jump in the temperatures used by Hirata and Yokokawa to above 695°C.In our present study we have used relatively coarse temperature increments (25°C)to monitor the general form of the phase transition,but then we have used much finer intervals (7°C)to probe the nature (first order or continuous)of the ferroelectric to paraelectric transition.We conclude that as a result of the relatively coarse temperature intervals used by Hirata and Yokokawa it was not possible for those authors to establish whether the ferroelectric to paraelec-tric transition in Bi 4Ti 3O 12was first order or continuous.The temperature dependence of the lattice parameters established using powder neutron diffraction data de-scribed by Lightfoot and Hervoches 16,29is very similar to that observed here for the data collected in 25°C intervals.On the basis of a similar density of data,Lightfoot and Hervoches 29concluded that the transition is first order.In comparison,our data collected in 7°C intervals using high-resolution synchrotron X-ray meth-ods strongly suggests the transition is continuous,albeit involving an intermediate phase.In conclusion we have identified the existence of an intermediate orthorhombic phase in the solid-state phase transition of the ferroelectric n )3Aurivillius phases Bi 4Ti 3O 12.Two possible orthorhombic phases were iden-tified using group theory,Fmm 2and Cmca ,depending on the sequence in which the two modes responsible for the lowering of symmetry condense.By analogy with the n )2oxide SrBi 2Ta 2O 9,the most likely sequence of transitions is B 2cb 670°C fCmca 695°CfI 4/mmm .Clearly confirming the existence of and establishing the precise structure of the proposed intermediate phase is of considerable interest,and efforts aimed at this are in progress.Acknowledgment.This work performed at the Australian National Beamline Facility was supported by the Australian Synchrotron Research Program,which is funded by the Commonwealth of Australia under the Major National Research Facilities program.B.J.K.acknowledges the support of the Australian Research Council.The assistance of Dr.James Hester at the ANBF is gratefully acknowledged.We thank Dr.P.Lightfoot for bringing ref 29to our attention while this manuscript was under review.CM034580L(28)Miller,S.C.;Love,W.F.Tables of Irreducible Representations of Space Groups and Co-representations of Magnetic Space Groups ;Pruett Press:Boulder,CO,1967.(29)Hervoches,C.H.;Lightfoot,P.Proceedings of CIMTEC,10th International Ceramics Congress ,Florence,Italy,July 2002.Figure 3.Schematic diagram showing the group -subgroup relationships for the n )3Aurivillius oxides.The solid lines show the transitions that are allowed to be continuous.The tilt system for the intermediate phases is given.5028Chem.Mater.,Vol.15,No.26,2003Zhou etal.。

公司的组织结构(英语)

Types of Organizational Structures
要点一
Flat Structure
要点二
Network Structure
A flat organization has few levels of management between the top executives and front line employees This structure emphasizes empowerment, teamwork, and quick decision making, empowering employees to take ownership of their work and collaborate directly with colleagues
Limited cross functional collaboration: The siloed nature of functional departments can hide collaboration and innovation
Potential for conflict: Competition for resources and power struggles between departments can create internal conflict
May create interdivisional periodic and competition
for resources
Can result in a lake of overall strategic direction
and coordination
Examples
A large consumer goods company with multiple product lines, such as personal care, home care, and food products, may organize its business into separate divisions for each product category

圆柱绕流尾迹对壁湍流相干结构影响的实验研究_姜楠

第21卷第3期2007年09月实验流体力学Journal of Experiments in Fluid MechanicsVol.21,No.3Sep.,2007文章编号:1672-9897(2007)03-0008-06圆柱绕流尾迹对壁湍流相干结构影响的实验研究X姜楠,李悦雷(天津大学力学系天津市现代工程力学重点实验室,天津300072)摘要:对边界层外区的圆柱尾迹流动结构对边界层近壁区相干结构的影响进行了实验研究。

实验在低湍流度风洞中进行,将圆柱放置于ycU1.1D(D为边界层厚度)处,利用热线风速仪分别测量了沿流向不同位置边界层内的瞬时脉动速度信号,并分别比较了位于x P d=1、2、3、4、5、10、15、20、30,y+=10~1000范围内的壁湍流相干结构条件相位平均波形及其统计特性。

发现圆柱绕流尾迹对平板边界层内相干结构有明显的影响,圆柱绕流尾迹虽然使壁湍流相干结构从喷射向扫掠转变阶段的强度减弱,但壁湍流相干结构的发生概率增加,总体上促进湍流产生,使湍流边界层增厚,壁面摩擦切应力和壁面摩擦速度均增加,从而肯定了湍流边界层外层流动中产生的扰动与近壁区相干结构猝发的生成和发展有直接联系,壁湍流相干结构猝发是外区流动中产生的扰动与湍流边界层内区共同作用产生的这一结论。

关键词:圆柱绕流尾迹;湍流边界层;近壁区域;相干结构;猝发中图分类号:O357文献标识码:AExperimental study on coherent structures in wall turbu lenceinteracting with a circular cylinder wakeJIANG Nan,LI Yue-lei(Tianjin Key Laboratory of Modern Engineering Mechanics,Department of Mechanics,Tianjin University,Tianjin300072,China)Abstract:The experiment is carried out to investigate coherent structures in the near wall region of turbu-lent boundary layer interacting with the wake of a circular cylinder in the outer region of turbulent boundaryla yer.The circular cylinder lies perpendicular to the mean flow direction,parallel to the wall and at the heightof y c U1.1D(where D is the thickness of the boundary layer).Time series of instantaneous velocity at differ-ent locations in normal direction and longitudinal direction in turbulent boundary layer have been finely mea-sured using ho-t wire ane mometer in a wind tunnel.Phase-averaged waveform and statistic character of coherentstructure in the region of x P d=10,20,30and y+=10~1000are acquired using wavelet transformation andconditional sampling method.The result shows that the effect of circular cylinder wake on coherent structure isevident.Although circular cylinder wake weakens the coherent structures.intensity in the course of transitionfrom eject to sweep,the probability of coherent structure generation increases,the turbulent boundary layer isthickened,the skin friction velocity and wall shear stress increase and turbulence production is promoted in general with the interaction of the circular cylinder wake.The direct relationship is further confirmed betweenproduction and evolution of coherent struc ture burst in wall turbulence and the disturbance in the outer regionof turbulent boundary layer.Burst of coherent structure in wall turbulence is the result of interacting betweenX收稿日期:2006-08-24;修订日期:2007-03-26基金项目:教育部新世纪人才基金,国家自然科学基金(10002011)、(10232020)联合资助项目.作者简介:姜楠(1968-),男,河南省封丘县人,天津大学力学系教授,博士生导师.主要从事湍流与实验流体力学研究.E-mail:nanj@tween the outer region disturbance and near -wall re gion of turbulent boundary layer.Key words :circular cylinder wake;turbulent boundary layer;near -wall region;coherent structure;burst0 引言自从斯坦福大学的Kline 小组(1967)[1]发现了湍流近壁区相干的大尺度快慢条纹结构,有关相干结构的发展与边界层的内层流动条件有关还是与边界层的外层流动条件有关的问题,一直还没有明确的结论。

中英文力学对准

一般力学类：分析力学 analytical mechanics拉格朗日乘子 Lagrange multiplier拉格朗日[量] Lagrangian拉格朗日括号 Lagrange bracket循环坐标 cyclic coordinate循环积分 cyclic integral哈密顿[量] Hamiltonian哈密顿函数 Hamiltonian function正则方程 canonical equation正则摄动 canonical perturbation正则变换 canonical transformation正则变量 canonical variable哈密顿原理 Hamilton principle作用量积分 action integral哈密顿-雅可比方程 Hamilton-Jacobi equation作用--角度变量 action-angle variables阿佩尔方程 Appell equation劳斯方程 Routh equation拉格朗日函数 Lagrangian function诺特定理 Noether theorem泊松括号 poisson bracket边界积分法 boundary integral method并矢 dyad运动稳定性 stability of motion轨道稳定性 orbital stability李雅普诺夫函数 Lyapunov function渐近稳定性 asymptotic stability结构稳定性 structural stability久期不稳定性 secular instability弗洛凯定理 Floquet theorem倾覆力矩 capsizing moment自由振动 free vibration固有振动 natural vibration暂态 transient state环境振动 ambient vibration反共振 anti-resonance衰减 attenuation库仑阻尼 Coulomb damping同相分量 in-phase component非同相分量 out-of -phase component超调量 overshoot 参量[激励]振动 parametric vibration模糊振动 fuzzy vibration临界转速 critical speed of rotation阻尼器 damper半峰宽度 half-peak width集总参量系统 lumped parameter system 相平面法 phase plane method相轨迹 phase trajectory等倾线法 isocline method跳跃现象 jump phenomenon负阻尼 negative damping达芬方程 Duffing equation希尔方程 Hill equationKBM方法 KBM method, Krylov-Bogoliu- bov-Mitropol'skii method马蒂厄方程 Mathieu equation平均法 averaging method组合音调 combination tone解谐 detuning耗散函数 dissipative function硬激励 hard excitation硬弹簧 hard spring, hardening spring谐波平衡法harmonic balance method久期项 secular term自激振动 self-excited vibration分界线 separatrix亚谐波 subharmonic软弹簧 soft spring ,softening spring软激励 soft excitation邓克利公式 Dunkerley formula瑞利定理 Rayleigh theorem分布参量系统 distributed parameter system优势频率 dominant frequency模态分析 modal analysis固有模态natural mode of vibration同步 synchronization超谐波 ultraharmonic范德波尔方程 van der pol equation频谱 frequency spectrum基频 fundamental frequencyWKB方法 WKB methodWKB方法Wentzel-Kramers-Brillouin method缓冲器 buffer风激振动 aeolian vibration嗡鸣 buzz倒谱cepstrum颤动 chatter蛇行 hunting阻抗匹配 impedance matching机械导纳 mechanical admittance机械效率 mechanical efficiency机械阻抗 mechanical impedance随机振动 stochastic vibration, random vibration隔振 vibration isolation减振 vibration reduction应力过冲 stress overshoot喘振surge摆振shimmy起伏运动 phugoid motion起伏振荡 phugoid oscillation驰振 galloping陀螺动力学 gyrodynamics陀螺摆 gyropendulum陀螺平台 gyroplatform陀螺力矩 gyroscoopic torque陀螺稳定器 gyrostabilizer陀螺体 gyrostat惯性导航 inertial guidance 姿态角 attitude angle方位角 azimuthal angle舒勒周期 Schuler period机器人动力学 robot dynamics多体系统 multibody system多刚体系统 multi-rigid-body system机动性 maneuverability凯恩方法Kane method转子[系统]动力学 rotor dynamics转子[一支承一基础]系统 rotor-support- foundation system静平衡 static balancing动平衡 dynamic balancing静不平衡 static unbalance动不平衡 dynamic unbalance现场平衡 field balancing不平衡 unbalance不平衡量 unbalance互耦力 cross force挠性转子 flexible rotor分频进动 fractional frequency precession半频进动half frequency precession油膜振荡 oil whip转子临界转速 rotor critical speed自动定心 self-alignment亚临界转速 subcritical speed涡动 whirl固体力学类：弹性力学 elasticity弹性理论 theory of elasticity均匀应力状态 homogeneous state of stress 应力不变量 stress invariant应变不变量 strain invariant应变椭球 strain ellipsoid均匀应变状态 homogeneous state of strain应变协调方程 equation of strain compatibility拉梅常量 Lame constants各向同性弹性 isotropic elasticity旋转圆盘 rotating circular disk 楔wedge开尔文问题 Kelvin problem布西内斯克问题 Boussinesq problem艾里应力函数 Airy stress function克罗索夫--穆斯赫利什维利法 Kolosoff- Muskhelishvili method基尔霍夫假设 Kirchhoff hypothesis板 Plate矩形板 Rectangular plate圆板 Circular plate环板 Annular plate波纹板 Corrugated plate加劲板 Stiffened plate,reinforcedPlate中厚板 Plate of moderate thickness弯[曲]应力函数 Stress function of bending 壳Shell扁壳 Shallow shell旋转壳 Revolutionary shell球壳 Spherical shell[圆]柱壳 Cylindrical shell锥壳Conical shell环壳 Toroidal shell封闭壳 Closed shell波纹壳 Corrugated shell扭[转]应力函数 Stress function of torsion 翘曲函数 Warping function半逆解法 semi-inverse method瑞利--里茨法 Rayleigh-Ritz method松弛法 Relaxation method莱维法 Levy method松弛 Relaxation量纲分析 Dimensional analysis自相似[性] self-similarity影响面 Influence surface接触应力 Contact stress赫兹理论 Hertz theory协调接触 Conforming contact滑动接触 Sliding contact滚动接触 Rolling contact压入 Indentation各向异性弹性 Anisotropic elasticity颗粒材料 Granular material散体力学 Mechanics of granular media热弹性 Thermoelasticity超弹性 Hyperelasticity粘弹性 Viscoelasticity对应原理 Correspondence principle褶皱Wrinkle塑性全量理论 Total theory of plasticity滑动 Sliding微滑Microslip粗糙度 Roughness非线性弹性 Nonlinear elasticity大挠度 Large deflection突弹跳变 snap-through有限变形 Finite deformation 格林应变 Green strain阿尔曼西应变 Almansi strain弹性动力学 Dynamic elasticity运动方程 Equation of motion准静态的Quasi-static气动弹性 Aeroelasticity水弹性 Hydroelasticity颤振Flutter弹性波Elastic wave简单波Simple wave柱面波 Cylindrical wave水平剪切波 Horizontal shear wave竖直剪切波Vertical shear wave体波 body wave无旋波 Irrotational wave畸变波 Distortion wave膨胀波 Dilatation wave瑞利波 Rayleigh wave等容波 Equivoluminal wave勒夫波Love wave界面波 Interfacial wave边缘效应 edge effect塑性力学 Plasticity可成形性 Formability金属成形 Metal forming耐撞性 Crashworthiness结构抗撞毁性 Structural crashworthiness 拉拔Drawing破坏机构 Collapse mechanism回弹 Springback挤压 Extrusion冲压 Stamping穿透Perforation层裂Spalling塑性理论 Theory of plasticity安定[性]理论 Shake-down theory运动安定定理 kinematic shake-down theorem静力安定定理 Static shake-down theorem 率相关理论 rate dependent theorem载荷因子load factor加载准则 Loading criterion加载函数 Loading function加载面 Loading surface塑性加载 Plastic loading塑性加载波 Plastic loading wave简单加载 Simple loading比例加载 Proportional loading卸载 Unloading卸载波 Unloading wave冲击载荷 Impulsive load阶跃载荷step load脉冲载荷 pulse load极限载荷 limit load中性变载 nentral loading拉抻失稳 instability in tension加速度波 acceleration wave本构方程 constitutive equation完全解 complete solution名义应力 nominal stress过应力 over-stress真应力 true stress等效应力 equivalent stress流动应力 flow stress应力间断 stress discontinuity应力空间 stress space主应力空间 principal stress space静水应力状态hydrostatic state of stress对数应变 logarithmic strain工程应变 engineering strain等效应变 equivalent strain应变局部化 strain localization应变率 strain rate应变率敏感性 strain rate sensitivity应变空间 strain space有限应变 finite strain塑性应变增量 plastic strain increment 累积塑性应变 accumulated plastic strain 永久变形 permanent deformation内变量 internal variable应变软化 strain-softening理想刚塑性材料 rigid-perfectly plastic Material刚塑性材料 rigid-plastic material理想塑性材料 perfectl plastic material 材料稳定性stability of material应变偏张量deviatoric tensor of strain应力偏张量deviatori tensor of stress 应变球张量spherical tensor of strain应力球张量spherical tensor of stress路径相关性 path-dependency线性强化 linear strain-hardening应变强化 strain-hardening随动强化 kinematic hardening各向同性强化 isotropic hardening强化模量 strain-hardening modulus幂强化 power hardening塑性极限弯矩 plastic limit bending Moment塑性极限扭矩 plastic limit torque弹塑性弯曲 elastic-plastic bending弹塑性交界面 elastic-plastic interface弹塑性扭转 elastic-plastic torsion粘塑性 Viscoplasticity非弹性 Inelasticity理想弹塑性材料 elastic-perfectly plastic Material极限分析 limit analysis极限设计 limit design极限面limit surface上限定理 upper bound theorem上屈服点upper yield point下限定理 lower bound theorem下屈服点 lower yield point界限定理 bound theorem初始屈服面initial yield surface后继屈服面 subsequent yield surface屈服面[的]外凸性 convexity of yield surface截面形状因子 shape factor of cross-section 沙堆比拟 sand heap analogy屈服Yield屈服条件 yield condition屈服准则 yield criterion屈服函数 yield function屈服面 yield surface塑性势 plastic potential能量吸收装置 energy absorbing device能量耗散率 energy absorbing device塑性动力学 dynamic plasticity塑性动力屈曲 dynamic plastic buckling塑性动力响应 dynamic plastic response塑性波 plastic wave运动容许场 kinematically admissible Field静力容许场 statically admissibleField流动法则 flow rule速度间断 velocity discontinuity滑移线 slip-lines滑移线场 slip-lines field移行塑性铰 travelling plastic hinge塑性增量理论 incremental theory ofPlasticity米泽斯屈服准则 Mises yield criterion普朗特--罗伊斯关系 prandtl- Reuss relation特雷斯卡屈服准则 Tresca yield criterion洛德应力参数 Lode stress parameter莱维--米泽斯关系 Levy-Mises relation亨基应力方程 Hencky stress equation赫艾--韦斯特加德应力空间Haigh-Westergaard stress space洛德应变参数 Lode strain parameter德鲁克公设 Drucker postulate盖林格速度方程Geiringer velocity Equation结构力学 structural mechanics结构分析 structural analysis结构动力学 structural dynamics拱 Arch三铰拱 three-hinged arch抛物线拱 parabolic arch圆拱 circular arch穹顶Dome空间结构 space structure空间桁架 space truss雪载[荷] snow load风载[荷] wind load土压力 earth pressure地震载荷 earthquake loading弹簧支座 spring support支座位移 support displacement支座沉降 support settlement超静定次数 degree of indeterminacy机动分析 kinematic analysis 结点法 method of joints截面法 method of sections结点力 joint forces共轭位移 conjugate displacement影响线 influence line三弯矩方程 three-moment equation单位虚力 unit virtual force刚度系数 stiffness coefficient柔度系数 flexibility coefficient力矩分配 moment distribution力矩分配法moment distribution method力矩再分配 moment redistribution分配系数 distribution factor矩阵位移法matri displacement method单元刚度矩阵 element stiffness matrix单元应变矩阵 element strain matrix总体坐标 global coordinates贝蒂定理 Betti theorem高斯--若尔当消去法 Gauss-Jordan elimination Method屈曲模态 buckling mode复合材料力学 mechanics of composites 复合材料composite material纤维复合材料 fibrous composite单向复合材料 unidirectional composite泡沫复合材料foamed composite颗粒复合材料 particulate composite层板Laminate夹层板 sandwich panel正交层板 cross-ply laminate斜交层板 angle-ply laminate层片Ply多胞固体 cellular solid膨胀 Expansion压实Debulk劣化 Degradation脱层 Delamination脱粘 Debond纤维应力 fiber stress层应力 ply stress层应变ply strain层间应力 interlaminar stress比强度 specific strength强度折减系数 strength reduction factor强度应力比 strength -stress ratio横向剪切模量 transverse shear modulus 横观各向同性 transverse isotropy正交各向异 Orthotropy剪滞分析 shear lag analysis短纤维 chopped fiber长纤维 continuous fiber纤维方向 fiber direction纤维断裂 fiber break纤维拔脱 fiber pull-out纤维增强 fiber reinforcement致密化 Densification最小重量设计 optimum weight design网格分析法 netting analysis混合律 rule of mixture失效准则 failure criterion蔡--吴失效准则 Tsai-W u failure criterion 达格代尔模型 Dugdale model断裂力学 fracture mechanics概率断裂力学 probabilistic fracture Mechanics格里菲思理论 Griffith theory线弹性断裂力学 linear elastic fracturemechanics, LEFM弹塑性断裂力学 elastic-plastic fracture mecha-nics, EPFM断裂 Fracture脆性断裂 brittle fracture解理断裂 cleavage fracture蠕变断裂 creep fracture延性断裂 ductile fracture晶间断裂 inter-granular fracture准解理断裂 quasi-cleavage fracture穿晶断裂 trans-granular fracture裂纹Crack裂缝Flaw缺陷Defect割缝Slit微裂纹Microcrack折裂Kink椭圆裂纹 elliptical crack深埋裂纹 embedded crack[钱]币状裂纹 penny-shape crack预制裂纹 Precrack 短裂纹 short crack表面裂纹 surface crack裂纹钝化 crack blunting裂纹分叉 crack branching裂纹闭合 crack closure裂纹前缘 crack front裂纹嘴 crack mouth裂纹张开角crack opening angle,COA裂纹张开位移 crack opening displacement, COD裂纹阻力 crack resistance裂纹面 crack surface裂纹尖端 crack tip裂尖张角 crack tip opening angle,CTOA裂尖张开位移 crack tip openingdisplacement, CTOD裂尖奇异场crack tip singularity Field裂纹扩展速率 crack growth rate稳定裂纹扩展 stable crack growth定常裂纹扩展 steady crack growth亚临界裂纹扩展 subcritical crack growth 裂纹[扩展]减速 crack retardation止裂crack arrest止裂韧度 arrest toughness断裂类型 fracture mode滑开型 sliding mode张开型 opening mode撕开型 tearing mode复合型 mixed mode撕裂 Tearing撕裂模量 tearing modulus断裂准则 fracture criterionJ积分 J-integralJ阻力曲线 J-resistance curve断裂韧度 fracture toughness应力强度因子 stress intensity factorHRR场 Hutchinson-Rice-Rosengren Field守恒积分 conservation integral有效应力张量 effective stress tensor应变能密度strain energy density能量释放率 energy release rate内聚区 cohesive zone塑性区 plastic zone张拉区 stretched zone热影响区heat affected zone, HAZ延脆转变温度 brittle-ductile transitiontemperature剪切带shear band剪切唇shear lip无损检测 non-destructive inspection双边缺口试件double edge notchedspecimen, DEN specimen单边缺口试件 single edge notchedspecimen, SEN specimen三点弯曲试件 three point bendingspecimen, TPB specimen中心裂纹拉伸试件 center cracked tension specimen, CCT specimen中心裂纹板试件 center cracked panelspecimen, CCP specimen紧凑拉伸试件 compact tension specimen, CT specimen大范围屈服large scale yielding小范围攻屈服 small scale yielding韦布尔分布 Weibull distribution帕里斯公式 paris formula空穴化 Cavitation应力腐蚀 stress corrosion概率风险判定 probabilistic riskassessment, PRA损伤力学 damage mechanics损伤Damage连续介质损伤力学 continuum damage mechanics细观损伤力学 microscopic damage mechanics累积损伤 accumulated damage脆性损伤 brittle damage延性损伤 ductile damage宏观损伤 macroscopic damage细观损伤 microscopic damage微观损伤 microscopic damage损伤准则 damage criterion损伤演化方程 damage evolution equation 损伤软化 damage softening损伤强化 damage strengthening 损伤张量 damage tensor损伤阈值 damage threshold损伤变量 damage variable损伤矢量 damage vector损伤区 damage zone疲劳Fatigue低周疲劳 low cycle fatigue应力疲劳 stress fatigue随机疲劳 random fatigue蠕变疲劳 creep fatigue腐蚀疲劳 corrosion fatigue疲劳损伤 fatigue damage疲劳失效 fatigue failure疲劳断裂 fatigue fracture疲劳裂纹 fatigue crack疲劳寿命 fatigue life疲劳破坏 fatigue rupture疲劳强度 fatigue strength疲劳辉纹 fatigue striations疲劳阈值 fatigue threshold交变载荷 alternating load交变应力 alternating stress应力幅值 stress amplitude应变疲劳 strain fatigue应力循环 stress cycle应力比 stress ratio安全寿命 safe life过载效应 overloading effect循环硬化 cyclic hardening循环软化 cyclic softening环境效应 environmental effect裂纹片crack gage裂纹扩展 crack growth, crack Propagation裂纹萌生 crack initiation循环比 cycle ratio实验应力分析 experimental stressAnalysis工作[应变]片 active[strain] gage基底材料 backing material应力计stress gage零[点]飘移zero shift, zero drift应变测量 strain measurement应变计strain gage应变指示器 strain indicator应变花 strain rosette应变灵敏度 strain sensitivity机械式应变仪 mechanical strain gage 直角应变花 rectangular rosette引伸仪 Extensometer应变遥测 telemetering of strain横向灵敏系数 transverse gage factor 横向灵敏度 transverse sensitivity焊接式应变计 weldable strain gage 平衡电桥 balanced bridge粘贴式应变计 bonded strain gage粘贴箔式应变计bonded foiled gage粘贴丝式应变计 bonded wire gage 桥路平衡 bridge balancing电容应变计 capacitance strain gage 补偿片 compensation technique补偿技术 compensation technique基准电桥 reference bridge电阻应变计 resistance strain gage温度自补偿应变计 self-temperature compensating gage半导体应变计 semiconductor strain Gage集流器slip ring应变放大镜 strain amplifier疲劳寿命计 fatigue life gage电感应变计 inductance [strain] gage 光[测]力学 Photomechanics光弹性 Photoelasticity光塑性 Photoplasticity杨氏条纹 Young fringe双折射效应 birefrigent effect等位移线 contour of equalDisplacement暗条纹 dark fringe条纹倍增 fringe multiplication干涉条纹 interference fringe等差线 Isochromatic等倾线 Isoclinic等和线 isopachic应力光学定律 stress- optic law主应力迹线 Isostatic亮条纹 light fringe 光程差optical path difference热光弹性 photo-thermo -elasticity光弹性贴片法 photoelastic coating Method光弹性夹片法 photoelastic sandwich Method动态光弹性 dynamic photo-elasticity空间滤波 spatial filtering空间频率 spatial frequency起偏镜 Polarizer反射式光弹性仪 reflection polariscope残余双折射效应 residual birefringent Effect应变条纹值 strain fringe value应变光学灵敏度 strain-optic sensitivity 应力冻结效应 stress freezing effect应力条纹值 stress fringe value应力光图 stress-optic pattern暂时双折射效应 temporary birefringent Effect脉冲全息法 pulsed holography透射式光弹性仪 transmission polariscope 实时全息干涉法 real-time holographicinterfero - metry网格法 grid method全息光弹性法 holo-photoelasticity全息图Hologram全息照相 Holograph全息干涉法 holographic interferometry 全息云纹法 holographic moire technique 全息术 Holography全场分析法 whole-field analysis散斑干涉法 speckle interferometry散斑Speckle错位散斑干涉法 speckle-shearinginterferometry, shearography散斑图Specklegram白光散斑法white-light speckle method云纹干涉法 moire interferometry[叠栅]云纹 moire fringe[叠栅]云纹法 moire method云纹图 moire pattern离面云纹法 off-plane moire method参考栅 reference grating试件栅 specimen grating分析栅 analyzer grating面内云纹法 in-plane moire method脆性涂层法 brittle-coating method条带法 strip coating method坐标变换 transformation ofCoordinates计算结构力学 computational structuralmecha-nics加权残量法weighted residual method有限差分法 finite difference method有限[单]元法 finite element method配点法 point collocation里茨法 Ritz method广义变分原理 generalized variational Principle最小二乘法 least square method胡[海昌]一鹫津原理 Hu-Washizu principle 赫林格-赖斯纳原理 Hellinger-Reissner Principle修正变分原理 modified variational Principle约束变分原理 constrained variational Principle混合法 mixed method杂交法 hybrid method边界解法boundary solution method有限条法 finite strip method半解析法 semi-analytical method协调元 conforming element非协调元 non-conforming element混合元 mixed element杂交元 hybrid element边界元 boundary element强迫边界条件 forced boundary condition 自然边界条件 natural boundary condition 离散化 Discretization离散系统 discrete system连续问题 continuous problem广义位移 generalized displacement广义载荷 generalized load广义应变 generalized strain广义应力 generalized stress界面变量 interface variable 节点 node, nodal point[单]元 Element角节点 corner node边节点 mid-side node内节点 internal node无节点变量 nodeless variable杆元 bar element桁架杆元 truss element梁元 beam element二维元 two-dimensional element一维元 one-dimensional element三维元 three-dimensional element轴对称元 axisymmetric element板元 plate element壳元 shell element厚板元 thick plate element三角形元 triangular element四边形元 quadrilateral element四面体元 tetrahedral element曲线元 curved element二次元 quadratic element线性元 linear element三次元 cubic element四次元 quartic element等参[数]元 isoparametric element超参数元 super-parametric element亚参数元 sub-parametric element节点数可变元 variable-number-node element拉格朗日元 Lagrange element拉格朗日族 Lagrange family巧凑边点元 serendipity element巧凑边点族 serendipity family无限元 infinite element单元分析 element analysis单元特性 element characteristics刚度矩阵 stiffness matrix几何矩阵 geometric matrix等效节点力 equivalent nodal force节点位移 nodal displacement节点载荷 nodal load位移矢量 displacement vector载荷矢量 load vector质量矩阵 mass matrix集总质量矩阵 lumped mass matrix相容质量矩阵 consistent mass matrix阻尼矩阵 damping matrix瑞利阻尼 Rayleigh damping刚度矩阵的组集 assembly of stiffnessMatrices载荷矢量的组集 consistent mass matrix质量矩阵的组集 assembly of mass matrices 单元的组集 assembly of elements局部坐标系 local coordinate system局部坐标 local coordinate面积坐标 area coordinates体积坐标 volume coordinates曲线坐标 curvilinear coordinates静凝聚 static condensation合同变换 contragradient transformation形状函数 shape function试探函数 trial function检验函数test function权函数 weight function样条函数 spline function代用函数 substitute function降阶积分 reduced integration零能模式 zero-energy modeP收敛 p-convergenceH收敛 h-convergence掺混插值 blended interpolation等参数映射 isoparametric mapping双线性插值 bilinear interpolation小块检验 patch test非协调模式 incompatible mode 节点号 node number单元号 element number带宽 band width带状矩阵 banded matrix变带状矩阵 profile matrix带宽最小化minimization of band width波前法 frontal method子空间迭代法 subspace iteration method 行列式搜索法determinant search method逐步法 step-by-step method纽马克法Newmark威尔逊法 Wilson拟牛顿法 quasi-Newton method牛顿-拉弗森法 Newton-Raphson method 增量法 incremental method初应变 initial strain初应力 initial stress切线刚度矩阵 tangent stiffness matrix割线刚度矩阵 secant stiffness matrix模态叠加法mode superposition method平衡迭代 equilibrium iteration子结构 Substructure子结构法 substructure technique超单元 super-element网格生成 mesh generation结构分析程序 structural analysis program 前处理 pre-processing后处理 post-processing网格细化 mesh refinement应力光顺 stress smoothing组合结构 composite structure流体动力学类：流体动力学 fluid dynamics连续介质力学 mechanics of continuous media介质medium流体质点 fluid particle无粘性流体 nonviscous fluid, inviscid fluid连续介质假设 continuous medium hypothesis流体运动学 fluid kinematics水静力学 hydrostatics 液体静力学 hydrostatics支配方程 governing equation伯努利方程 Bernoulli equation伯努利定理 Bernonlli theorem毕奥-萨伐尔定律 Biot-Savart law欧拉方程Euler equation亥姆霍兹定理 Helmholtz theorem开尔文定理 Kelvin theorem涡片 vortex sheet库塔-茹可夫斯基条件 Kutta-Zhoukowskicondition布拉休斯解 Blasius solution达朗贝尔佯廖 d'Alembert paradox 雷诺数 Reynolds number施特鲁哈尔数 Strouhal number随体导数 material derivative不可压缩流体 incompressible fluid 质量守恒 conservation of mass动量守恒 conservation of momentum 能量守恒 conservation of energy动量方程 momentum equation能量方程 energy equation控制体积 control volume液体静压 hydrostatic pressure涡量拟能 enstrophy压差 differential pressure流[动] flow流线stream line流面 stream surface流管stream tube迹线path, path line流场 flow field流态 flow regime流动参量 flow parameter流量 flow rate, flow discharge涡旋 vortex涡量 vorticity涡丝 vortex filament涡线 vortex line涡面 vortex surface涡层 vortex layer涡环 vortex ring涡对 vortex pair涡管 vortex tube涡街 vortex street卡门涡街 Karman vortex street马蹄涡 horseshoe vortex对流涡胞 convective cell卷筒涡胞 roll cell涡 eddy涡粘性 eddy viscosity环流 circulation环量 circulation速度环量 velocity circulation 偶极子 doublet, dipole驻点 stagnation point总压[力] total pressure总压头 total head静压头 static head总焓 total enthalpy能量输运 energy transport速度剖面 velocity profile库埃特流 Couette flow单相流 single phase flow单组份流 single-component flow均匀流 uniform flow非均匀流 nonuniform flow二维流 two-dimensional flow三维流 three-dimensional flow准定常流 quasi-steady flow非定常流unsteady flow, non-steady flow 暂态流transient flow周期流 periodic flow振荡流 oscillatory flow分层流 stratified flow无旋流 irrotational flow有旋流 rotational flow轴对称流 axisymmetric flow不可压缩性 incompressibility不可压缩流[动] incompressible flow 浮体 floating body定倾中心metacenter阻力 drag, resistance减阻 drag reduction表面力 surface force表面张力 surface tension毛细[管]作用 capillarity来流 incoming flow自由流 free stream自由流线 free stream line外流 external flow进口 entrance, inlet出口exit, outlet扰动 disturbance, perturbation分布 distribution传播 propagation色散 dispersion弥散 dispersion附加质量added mass ,associated mass收缩 contraction镜象法 image method无量纲参数 dimensionless parameter几何相似 geometric similarity运动相似 kinematic similarity动力相似[性] dynamic similarity平面流 plane flow势 potential势流 potential flow速度势 velocity potential复势 complex potential复速度 complex velocity流函数 stream function源source汇sink速度[水]头 velocity head拐角流 corner flow空泡流cavity flow超空泡 supercavity超空泡流 supercavity flow空气动力学 aerodynamics低速空气动力学 low-speed aerodynamics 高速空气动力学 high-speed aerodynamics 气动热力学 aerothermodynamics亚声速流[动] subsonic flow跨声速流[动] transonic flow超声速流[动] supersonic flow锥形流 conical flow楔流wedge flow叶栅流 cascade flow非平衡流[动] non-equilibrium flow细长体 slender body细长度 slenderness钝头体 bluff body钝体 blunt body翼型 airfoil翼弦 chord薄翼理论 thin-airfoil theory构型 configuration后缘 trailing edge迎角 angle of attack失速stall脱体激波detached shock wave 波阻wave drag诱导阻力 induced drag诱导速度 induced velocity临界雷诺数critical Reynolds number前缘涡 leading edge vortex附着涡 bound vortex约束涡 confined vortex气动中心 aerodynamic center气动力 aerodynamic force气动噪声 aerodynamic noise气动加热 aerodynamic heating离解 dissociation地面效应 ground effect气体动力学 gas dynamics稀疏波 rarefaction wave热状态方程thermal equation of state喷管Nozzle普朗特-迈耶流 Prandtl-Meyer flow瑞利流 Rayleigh flow可压缩流[动] compressible flow可压缩流体 compressible fluid绝热流 adiabatic flow非绝热流 diabatic flow未扰动流 undisturbed flow等熵流 isentropic flow匀熵流 homoentropic flow兰金-于戈尼奥条件 Rankine-Hugoniot condition状态方程 equation of state量热状态方程 caloric equation of state完全气体 perfect gas拉瓦尔喷管 Laval nozzle马赫角 Mach angle马赫锥 Mach cone马赫线Mach line马赫数Mach number马赫波Mach wave当地马赫数 local Mach number冲击波 shock wave激波 shock wave正激波normal shock wave斜激波oblique shock wave头波 bow wave附体激波 attached shock wave激波阵面 shock front激波层 shock layer压缩波 compression wave反射 reflection折射 refraction散射scattering衍射 diffraction绕射 diffraction出口压力 exit pressure超压[强] over pressure反压 back pressure爆炸 explosion爆轰 detonation缓燃 deflagration水动力学 hydrodynamics液体动力学 hydrodynamics泰勒不稳定性 Taylor instability 盖斯特纳波 Gerstner wave斯托克斯波 Stokes wave瑞利数 Rayleigh number自由面 free surface波速 wave speed, wave velocity 波高 wave height波列wave train波群 wave group波能wave energy表面波 surface wave表面张力波 capillary wave规则波 regular wave不规则波 irregular wave浅水波 shallow water wave深水波deep water wave重力波 gravity wave椭圆余弦波 cnoidal wave潮波tidal wave涌波surge wave破碎波 breaking wave船波ship wave非线性波 nonlinear wave孤立子 soliton水动[力]噪声 hydrodynamic noise 水击 water hammer空化 cavitation空化数 cavitation number 空蚀 cavitation damage超空化流 supercavitating flow水翼 hydrofoil水力学 hydraulics洪水波 flood wave涟漪ripple消能 energy dissipation海洋水动力学 marine hydrodynamics谢齐公式 Chezy formula欧拉数 Euler number弗劳德数 Froude number水力半径 hydraulic radius水力坡度 hvdraulic slope高度水头 elevating head水头损失 head loss水位 water level水跃 hydraulic jump含水层 aquifer排水 drainage排放量 discharge壅水曲线back water curve压[强水]头 pressure head过水断面 flow cross-section明槽流open channel flow孔流 orifice flow无压流 free surface flow有压流 pressure flow缓流 subcritical flow急流 supercritical flow渐变流gradually varied flow急变流 rapidly varied flow临界流 critical flow异重流density current, gravity flow堰流weir flow掺气流 aerated flow含沙流 sediment-laden stream降水曲线 dropdown curve沉积物 sediment, deposit沉[降堆]积 sedimentation, deposition沉降速度 settling velocity流动稳定性 flow stability不稳定性 instability奥尔-索末菲方程 Orr-Sommerfeld equation 涡量方程 vorticity equation泊肃叶流 Poiseuille flow奥辛流 Oseen flow剪切流 shear flow粘性流[动] viscous flow层流 laminar flow分离流 separated flow二次流 secondary flow近场流near field flow远场流 far field flow滞止流 stagnation flow尾流 wake [flow]回流 back flow反流 reverse flow射流 jet自由射流 free jet管流pipe flow, tube flow内流 internal flow拟序结构 coherent structure 猝发过程 bursting process表观粘度 apparent viscosity 运动粘性 kinematic viscosity 动力粘性 dynamic viscosity 泊 poise厘泊 centipoise厘沱 centistoke剪切层 shear layer次层 sublayer流动分离 flow separation层流分离 laminar separation 湍流分离 turbulent separation 分离点 separation point附着点 attachment point再附 reattachment再层流化 relaminarization起动涡starting vortex驻涡 standing vortex涡旋破碎 vortex breakdown 涡旋脱落 vortex shedding压[力]降 pressure drop压差阻力 pressure drag压力能 pressure energy型阻 profile drag滑移速度 slip velocity无滑移条件 non-slip condition 壁剪应力 skin friction, frictional drag壁剪切速度 friction velocity磨擦损失 friction loss磨擦因子 friction factor耗散 dissipation滞后lag相似性解 similar solution局域相似 local similarity气体润滑 gas lubrication液体动力润滑 hydrodynamic lubrication 浆体 slurry泰勒数 Taylor number纳维-斯托克斯方程 Navier-Stokes equation 牛顿流体 Newtonian fluid边界层理论boundary later theory边界层方程boundary layer equation边界层 boundary layer附面层 boundary layer层流边界层laminar boundary layer湍流边界层turbulent boundary layer温度边界层thermal boundary layer边界层转捩boundary layer transition边界层分离boundary layer separation边界层厚度boundary layer thickness位移厚度 displacement thickness动量厚度 momentum thickness能量厚度 energy thickness焓厚度 enthalpy thickness注入 injection吸出suction泰勒涡 Taylor vortex速度亏损律 velocity defect law形状因子 shape factor测速法 anemometry粘度测定法 visco[si] metry流动显示 flow visualization油烟显示 oil smoke visualization孔板流量计 orifice meter频率响应 frequency response油膜显示oil film visualization阴影法 shadow method纹影法 schlieren method烟丝法smoke wire method丝线法 tuft method。

语言学Chapter4课后练习答案(20200602074319)

Chapter 4 Revision Exercises1. What is syntax?Syntax is a branch of linguistics that studies how words are combined to form sentences and the rules that govern the formation of sentences.2. What is phrase structure rule?The grammatical mechanism that regulates the arrangement of elements (i.e. specifiers, heads, and complements) that make up a phrase is called a phrase structure rule.The phrase structural rule for NP, VP, AP, and PP can be written as follows: NP→(Det) N (PP) ...VP→(Qual) V (NP) ...AP→(Deg) A (PP) ...PP→(Deg) P (NP) ...We can formulate a single general phrasal structural rule in which X stands for the head N, V, A or P.The XP rule: XP→(specifier) X (complement)3. What is category? How to determine a word’s category?Category refers to a group of linguistic items which fulfill the same or similar functions in a particular language such as a sentence, a noun phrase or a verb.To determine a word's category, three criteria are usually employed, namely meaning, inflection and distribution. The most reliable of determining a word’s category is its distribution.4. What is coordinate structure and what properties does it have?The structure formed by joining two or more elements of the same type with the help of a conjunction is called coordinate structure.It has four important properties:1)there is no limit on the number of coordinated categories that can appearprior to the conjunction.2) a category at any level a head or an entire XP can be coordinated.3)coordinated categories must be of the same type.4)the category type of the coordinate phrase is identical to the categorytype of the elements being conjoined.5. What elements does a phrase contain and what role does each element play?A phrase usually contains the following elements: head, specifier and complement. Sometimes it also contains another kind of element termed modifier.The role each element can play:Head:Head is the word around which a phrase is formed.Specifier:Specifier has both special semantic and syntactic roles. Semantically, it helps to make more precise the meaning of the head. Syntactically, it typically marks a phrase boundary.Complement:Complements are themselves phrases and provide information about entities and locations whose existence is implied by the meaning of the head.Modifier:Modifiers specify optionally expressible properties of the heads.6. What is deep structure and what is surface structure?There are two levels of syntactic structure. The first, formed by the XP rule in accordance with the head's subcategorization properties, is called deep structure (or D-structure). The second, corresponding to the final syntactic form of the sentence which results from appropriate transformations, is called surface structure (or S-structure).7. Indicate the category of each word in the following sentences.a) The old lady got off the bus carefully.Det A N V P Det N Advb) The car suddenly crashed onto the river bank.Det N Adv V P Det Nc) The blinding snowstorm might delay the opening of the schools.Det A N Aux V Det N P Det Nd) This cloth feels quite soft.Det N V Deg A8. The following phrases include a head, a complement, and a specifier. Draw the appropriate tree structure for each phrase.a) rich in mineralsAPA PPrich in mineralsb) often read detective storiesVPQual V NPoften read detective storiesc) the argument against the proposalsNPDet N PPthe argument against the proposals d) already above the windowPPDeg P NPalready above the window9. The following sentences contain modifiers of various types. For each sentences, first identify the modifier(s), then draw the tree sentences.a) A crippled passenger landed the airplane with extreme caution. Modifiers: crippled(AdjP), with extreme caution(PP)SNP Infl VPAPDet A N Pst V NPDet N PPP NPAP NAA crippled passenger landed the airplane with extreme cautionb) A huge moon hung in the black sky.Modifiers: huge(AdjP), in the black sky(PP)SNP Infl VPDet AP N Pst V PPA P NPDet AP NA huge moon hung in the black skyc) The man examined his car carefully yesterday.Modifiers: carefully(AdvP), yesterday(AdvP)SNP Infl VPDet N Pst V NP AdvPDet N AdvP AdvAdv The man examined his car carefully yesterdayd) A wooden hut near the lake collapsed in the storm.Modifiers: wooden(AdjP), in the storm(PP)SNP Infl VPDet AP N PP Pst V PPA P NP P NPDet N Det NA wooden hut near the lake collapsed in the storm10. The following sentences all contain conjoined categories. Draw a tree structure for each of the sentences.a) Jim has washed the dirty shirts and pants.SNP Infl VPN V NPDet AP N Con NAJim has washed the dirty shirts and pantsb) Helen put on her clothes and went out.SNP Infl VPN Pst V PP Con V PPP NP PDet NHelen put on her clothes and went outc) Mary is fond of literature but tired of statistics.SNP Infl VPN Pre V AP Con APA PP A PPP NP P NPN N Mary is fond of literature but tired of statistics11. The following sentences all contain embedded clauses that function as complements of a verb, an adjective, a preposition or a noun. Draw a tree structure for each sentence.a) You know that I hate war.SNP Infl VPN Pre V NPCPC SNP Infl VPNP N Pre V NPN You know that I hate war b) Gerry believes the fact that Anna flunked the English exam.SNP Infl VPN Pre V NPDet N CP-C SNP Infl VPNP N Pst V NPDet AP NAGerry believes the fact that Anna flunked the English examc) Chris was happy that his father bought him a Rolls-Royce.SNP Infl VPN Pst V APA CPC SNP NP Infl VPDet N Pst V NPN Det N Chris was happy that his father bought him aRoll-Royced) The children argued over whether bats had wings.SNP Infl VPDet N Pst V PPP CPC SNP Infl VPN Plu V NPNThe children argued over whether bats had wings 12. Each of the following sentences contains a relative clause. Draw the deep structure and the surface structure for each of these sentences.a) The essay that he wrote was excellent.Deep Structure:CPC SNP Infl VPDet N CP Pst V APC S Aux ANP Infl VPN Pst V NPNThe essay he wrote that was excellent Surface Structure:CPC SNP Infl VPDet N CP Pst V APC S Aux ANP NP Infl VPN N Pst V NPNThe essay that he wrote e was excellentb) Herbert bought a house that she loved.Deep Structure:CPC SNP Infl VPN Pst V NPDet N CPC SNP Infl VPN Pst V NPN Herbert bought a house she loved thatSurface Structure: CPC SNP Infl VPN Pst V NPDet N CPC SNP NP Infl VPN N Pst V NPN Herbert bought a house that she lovedec) The girl whom he adores majors in linguistics.Deep Structure:CPC SNP Infl VPDet N CP Pre V PPC S P NPNP Infl VP NN Pre V NPNThe girl he adores whom majors in linguisticsSurface Structure:CPC SNP Infl VPDet N CP Pre V PPNP C S P NPNP Infl VP NN N Pre V NPNThe girl whom he adores e majors in linguistics13. The derivations of the following sentences involve the inversion transformation. Give the deep structure and the surface structure of each sentence.a) Would you come tomorrow?Deep Structure:CPC SNP Infl VPN Aux V AdvPAdvYou would come tomorrowSurface Structure:CPC SInfl NP Infl VPAux N Aux V AdvPAdvWould You e come tomorrowb) What did Helen bring to the party?Deep Structure:CPC SNP Infl VPN Pst V NPN PPP Det NPNHelen did bring what to the party Surface Structure: CPC SNP Infl NP Infl VPN Pst N Pst V NPN PPP Det NPN What did Helen e bring e to the partyc) Who broke the window?Deep Structure:CPC SNP Infl VPN Pst V NPDet NWho broke the windowSurface Structure: CPC SNP NP Infl VPN N Pst V NPDet N Who e broke the window。

结构振动与动态子结构方法书英文

结构振动与动态子结构方法书英文Structural Vibrations and Dynamic Substructuring Methods.Structural vibrations are a fundamental aspect of many engineering disciplines, ranging from civil engineering to aerospace applications. These vibrations can be caused by various external forces such as wind, earthquake, or machine operations. Understanding and predicting these vibrations is crucial for ensuring the safety, efficiency, and durability of structures.Dynamic substructuring methods are a set of techniques used to analyze complex structures by dividing them into smaller, more manageable substructures. This approach allows for efficient numerical modeling and simulation of vibrations, particularly in large-scale systems where traditional methods may be computationally intensive.Basics of Structural Vibrations.Structural vibrations occur when a structure is subjected to external forces that cause it to move or deform. These forces can be periodic, such as those caused by rotating machinery, or non-periodic, such as those resulting from earthquakes. The response of the structure, including its displacement, velocity, and acceleration, is dependent on its mass, stiffness, and damping characteristics.The natural frequencies and mode shapes of a structure are key parameters in understanding its vibration behavior. Natural frequencies represent the resonant frequencies at which the structure tends to vibrate, while mode shapes describe the pattern of vibration at each frequency. These parameters can be obtained through modal analysis, which involves exciting the structure and measuring its response.Dynamic Substructuring Methods.Dynamic substructuring methods are based on the principle of modal synthesis. Instead of modeling theentire structure as a single, complex system, the structure is divided into smaller substructures, each with its own set of natural frequencies and mode shapes. These substructures are then coupled together to form the complete structure.One of the most commonly used dynamic substructuring methods is the fixed-interface modal synthesis. In this approach, the substructures are assumed to have fixed interfaces with each other, and the vibrations at these interfaces are used to couple the substructures. This allows for efficient modeling of the overall structure by reducing the number of degrees of freedom required for analysis.Another popular method is the free-interface modal synthesis, where the substructures are allowed to have free interfaces. This approach provides more flexibility in modeling the interactions between substructures but requires more complex coupling techniques.Applications of Dynamic Substructuring.Dynamic substructuring methods find applications in various engineering fields. In civil engineering, they are used to analyze the vibrations of bridges, buildings, and towers. In aerospace engineering, these methods are employed to study the dynamic behavior of aircraft and spacecraft. In mechanical engineering, dynamic substructuring is used to model and simulate the vibrations of machines and components.The key advantage of dynamic substructuring is its efficiency. By dividing a complex structure into smaller substructures, it becomes easier to model and analyze each substructure separately. This reduces the computational requirements and allows for faster simulation of theoverall structure. Additionally, the method provides a modular approach to modeling, where new substructures can be easily added or replaced without affecting the existing model.Challenges and Future Directions.Despite its advantages, dynamic substructuring methods also face some challenges. One of the main challenges is the accurate modeling of interface interactions between substructures. Achieving accurate coupling requires careful consideration of the boundary conditions and interface dynamics.Another challenge is the scalability of these methods to even larger and more complex structures. As the size and complexity of structures increase, so does the computational demand for analysis. Future research in dynamic substructuring could focus on developing more efficient algorithms and optimization techniques to handle these larger systems.In conclusion, structural vibrations and dynamic substructuring methods play a crucial role in understanding and predicting the dynamic behavior of structures. By dividing complex structures into manageable substructures, these methods enable efficient modeling and simulation, leading to safer, more efficient, and durable structures. Future research and advancements in this field willcontinue to push the boundaries of structural analysis and design.。

a由来

Lect., School of the Built Environment, The Univ. of Nottingham, Univ. Park, Nottingham NG7 2RD, UK. E-mail: Jianfei.Chen@ 2 Prof., Dept. of Civ. and Struct. Engrg., The Hong Kong Polytechnic Univ., Hong Kong, China. E-mail: cejgteng@.hk Note. Associate Editor: Joseph Bracci. Discussion open until December 1, 2001. To extend the closing date one month, a written request must be ﬁled with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on March 29, 2000; revised February 1, 2001. This paper is part of the Journal of Structural Engineering, Vol. 127, No. 7, July, 2001. ᭧ASCE, ISSN 0733-9445/01/0007-0784–0791/$8.00 ϩ $.50 per page. Paper No. 22327.
ANCHORAGE STRENGTH MODELS FOR FRP AND STEEL PLATES BONDED TO CONCRETE

Breaking Abstractions and Unstructuring Data Structures

Breaking Abstractions and Unstructuring Data Structures Christian Collberg Clark Thomborson Douglas LowDepartment of Computer Science,The University of Auckland,Private Bag92019,Auckland,New Zealand.collberg,cthombor,dlow001@AbstractTo ensure platform independence,mobile programs are distributed in forms that are isomorphic to the original source code.Such codes are easy to decompile,and hence they increase the risk of malicious reverse engineering at-tacks.Code obfuscation is one of several techniques which has been proposed to alleviate this situation.An obfuscator is a tool which–through the application of code transforma-tions–converts a program into an equivalent one that is more difﬁcult to reverse engineer.In a previous paper[5]we have described the design of a controlﬂow obfuscator for Java.In this paper we extend the design with transformations that obfuscate data structures and abstractions.In particular,we show how to obfuscate classes,arrays,procedural abstractions and built-in data types like strings,integers,and booleans.1IntroductionMobile programs are distributed in architecture-neutral formats(such as Java bytecode[8])that contain much of the same information as the original source code.While this achieves platform independence,it also makes pro-grams easy to decompile and reverse engineer.This is of particular concern to small software devel-opers who can ill afford to protect their software secrets through legal[17]means against larger and more powerful competitors[12].As an alternative,several forms of tech-nical[1,7]protection against theft of software secrets have been suggested:Server-Side Execution The user connects to the software developer’s site to run the program remotely,paying a small amount of electronic money every time.A soft-ware thief will never gain physical access to the appli-cation and will be unable to reverse engineer it.The downside is that the application will perform much worse than if it had run locally.Native Code When down-loading the application,the user’s site identiﬁes its architecture,and the corre-sponding native code version of the application is transmitted.Digital signatures should be attached to the code to assure authenticity and harmlessness.De-compilation of the native code is still possible[3],but much more difﬁcult,if,as is usual,symbol naming and type information is suppressed.Encryption Encrypting[11,21]the application will only protect against theft if the entire decryption/execution process takes place in hardware.If the code is exe-cuted in software by a virtual machine interpreter it will always be possible to intercept and decompile the decrypted code.Obfuscation Before distributing the application,the soft-ware developer runs it through an automatic obfusca-tor.This tool transforms the program into one that is functionally identical to the original but which is more difﬁcult to decompile and reverse engineer.Unlike server-side execution and hardware-based en-cryption schemes,code obfuscation can never completely protect an application from malicious reverse engineering efforts.Rather,obfuscation should be seen as a cheap way of making reverse engineering so technically difﬁcult that it becomes economically infeasible.To ensure this,the techniques employed by an obfuscator have to be powerful enough to thwart attacks by automatic deobfuscators that attempt to undo the obfuscating transformations.The remainder of the paper will examine various code transformations that obfuscate the abstractions and data structures used in an application.The paper is structured as follows.In Section2we give a brief overview of the design of a code obfuscator for Java which is currently under con-struction.Section3describes the criteria used to evaluate different types of obfuscating transformations.Sections4, 5,and6present a catalogue of obfuscating transformations. Section7summarizes our results.2The design of a Java obfuscatorFigure1outlines the design of our Java obfuscation tool. In aﬁrst phase the obfuscator reads and parses all refer-Figure1:Architecture of a Java obfuscator.a)transforms source program into target program,b)and have the same observable behavior(exceptin cases of non-termination or error-termination),and c)is a potent transformation,i.e.it renders moreobscure than.Observable behavior is deﬁned loosely as“behavior as experienced by the user.”This means that may have side-effects(such as creatingﬁles,sending messages over the Internet,etc.)that does not,as long as these side effects are not experienced by the user.Note that we do not require and to equally efﬁcient.In fact,many of our transformations will result in being slower or using more memory than.3.1Transformation qualityCollberg[5]also introduces the concept of quality of an obfuscating transformation,a combination of four mea-sures:potency The potency of measures how much more ob-scure(or complex or unreadable)renders the appli-cation.resilience The resilience of measures how well the transformation holds up under attack from an auto-matic deobfuscator.Some highly resilient transforma-tions are one-way,in the sense that they can never be undone.This is typically because they remove infor-mation(such as variable names or abstractions)from the program.Other transformations add useless in-formation to the program that does not change its ob-servable behavior,but which increases the“informa-tion load”on a human reader.These transformations can be undone with varying degrees of difﬁculty. stealth The stealth of measures how well obfuscated code blends in with the rest of the program.If intro-duces new code that differs wildly from what is in the original program it will be easy to spot for a reverse engineer.cost The cost of measures the execution time/space penalty which a transformation incurs on an obfus-cated application.While some trivial transformations (such as scrambling identiﬁers)are free(i.e.they in-cur no run-time cost)many of the transformations pre-sented in this paper will incur a varying amount of overhead.3.2Increasing potencyBefore we can design any obfuscating transformations we mustﬁrst deﬁne what it means for a program to be more obscure than a program.Any such measure of po-tency will,at best,be approximate since we cannot hope to measure exactly a human’s ability to understand a program.Fortunately,we can draw upon the vast body of work in the Software Complexity Metrics branch of Software En-gineering.The detailed complexity formulas found in the metrics’literature are of little interest to us,but they can be used to derive general statements such as:“if programs and are identical except that contains more of prop-erty than,then is more complex than.”Given such a statement,we can attempt to construct a transfor-mation which adds more of the-property to a program, knowing that this is likely to increase its obscurity.Of particular interest to us are the Henry[10],Chi-damber[2],and Munson[14]metrics.The Munson metric states that the complexity of a pro-gram increases with the complexity of the static data structures declared in.The complexity of a scalar vari-able is constant;the complexity of an array increases with the number of dimensions and with the complexity of the element type;and the complexity of a record increases with the number and complexity of itsﬁelds.The Henry metric states that the complexity of a func-tion increases with the number of formal parameters to ,and with the number of global data structures read or updated by.The Chidamber metric applies to object oriented pro-grams.The complexity of a class increases with the number of methods in,the depth(distance from the root) of in the inheritance tree,the number of other classes to which is coupled,and the number of methods that can be executed in response to a message sent to an object of .Other metrics express that the complexity of a pro-gram grows with the number of predicates it contains(Mc-Cabe[13])and with the nesting level of conditional and looping constructs(Harrison[9]).3.3Classifying transformationsThere are some aspects of program understandability that are not covered directly by software metrics.For ex-ample,it should be obvious that there is much valuable in-formation about a program in comments,strings,and iden-tiﬁers,although these do not enter into any metrics for-mula.Similarly,according to the Munson metric a two-dimensional array is more complex than a one-dimensional one.This fails to capture the fact that a programmer who declares a two-dimensional array does so for a purpose:the chosen structure somehow maps cleanly to the data that is being manipulated.If the array is folded into a one-dimensional structure the Munson metric would indicate that the transformed program is less complex than the orig-inal one,when,in fact,much useful information has been lost.With this in mind we can attempt to classify obfuscat-ing transformations according to the kind of information they yout transformations are typical of current Java obfuscators such as Crema[20].They remove source code formatting and scramble identiﬁers.Control trans-formations increase the McCabe and Harrison metrics by introducing predicated branches.Data transformations in-crease the Munson,Henry,or Chidamber metrics.Abstrac-tion transformations remove programmer-deﬁned abstrac-tions or introduce spurious ones.In this paper we describe transformations that obfuscate built-in data types and data and procedural abstractions in-troduced by the programmer.3.4Opaque predicatesMost control transformations and,as we will see,some data transformations,rely on the existence of opaque rmally,a predicate is opaque if its value is known a priori to the obfuscator,but this value is difﬁcult for the deobfuscator to deduce.For a predicate we write ()if always evaluates to().As an example,consider the following transformation where the obfuscator has introduced a bogus if-statement: In spite of the introduced if-statement,statement will always execute.The reason is that the opaque predicatewill always evaluate to.The trans-formed code in this example is resilient to attack by any deobfuscator ignorant of elementary number theory. Being able to create opaque predicates which are dif-ﬁcult for an obfuscator to crack is a major challenge to a creator of obfuscation tools,and the key to many highly resilient obfuscating transformations.Collberg[5] shows how it is possible to manufacture cheap and resilient opaque predicates based on intractable problems such as alias analysis.4Obfuscating data abstractionsIn this section we will discuss transformations that ob-scure the data abstractions used in the source application. Most of the transformations are designed to directly in-crease the Munson or Chidamber metrics.4.1Modify inheritance relationsIn current object-oriented languages such as Java,the main modularization and abstraction concept is the class.Classes are essentially abstract data types that encapsulate data(instance variables)and control(methods).We write a class as,where is the set of’s instance variables and its methods.In contrast to the traditional notion of abstract data types, two classes and can be composed by aggregation (has an instance variable of type)as well as by inher-itance(extends by adding new methods and instance variables).Borrowing the notation used in[18],we write inheritance as.is said to inherit from ,its super-or parent class.The operator is the func-tion that combines the parent class with the new proper-ties deﬁned in.The exact semantics of depends on the particular programming language.In languages such as Java,is usually interpreted as union when applied to the instance variables and as overriding when applied to methods.Extending the inheritance hierarchy tree.According to the Chidamber metric,the complexity of a class grows with its depth(distance from the root)in the inheritance hierarchy,and the number of its direct descendants.As shown in Figures2(a)and(b),there are two basic ways in which we can increase this complexity:we can split up (factor)a class or insert a new,bogus,class.When,as in Figure2(a),we factor a class into classes and we cannot arbitrarily move’s methods and instance variables into the resulting classes.To see this,letwhere method references instance variable.Any factoring of must respect the scope of .For example,we cannot factor into and where,,and. To deal with this problem we build a dependence graph for class.The nodes of are the members of,and itself.There is an edge in if the declaration of must be in scope for.If there is a path in, then must be declared in the child class.If there is a path in then either and are both declared in the same class or is declared in the parent class.See Figure3for an example.Another problem with class factoring is its low re-silience;there is nothing stopping a deobfuscator from sim-ply merging the factored classes.To prevent this,factor-ing and insertion are normally combined as shown in Fig-ure2(d).We can also insert bogus code which appears to create instances of all introduced classes.For example,the statement appears to create an in-stance of class.False refactoring.Figure2(c)shows a variant of class insertion,called false refactoring.Refactoring is a (sometimes automatic)technique for restructuring object-oriented programs whose structure has deteriorated[15]. Refactoring is a two-step process.First,it is detected(a)(b)(c)(d)Figure2:Modiﬁcations of the inheritance hierarchy.is the root of the inheritance tree(in Java).Triangles represent subtrees.There is an arrow from class to if inherits from.The two basic operations,class factoring and class insertion,are shown in(a)and(b),respectively.After factoring class,all references to in the program should be replaced by.Factoring and insertion are normally combined.This is done in(d),where the original class isﬁrst split into and,and then an extra child is created for.In(c)two classes and without common behavior are given the same bogus parent.Figure3:Example of a dependency graph built to facilitate class factoring.,and the constructor must all be de-clared in the child class.and may either be declared in the parent or the child class,but if is put into the child class then so must.1Thanks to Buz for pointing this out.just inline the code for each bytecode instruction prior to decompilation.There are two ways to increase the re-silience.First,the bytecode string could be converted to a program that produces it,as explained in Section6.2. Secondly,the original code can itself be obfuscated–for example by inserting bogus predicated branches protected by opaque predicates–prior to being translated to the spe-cialized bytecode.This is illustrated by transformationin Figure5.5.2Inline and outline methodsInlining is,of course,a important code optimization technique.It is also an extremely useful obfuscating trans-formation since it removes procedural abstractions from the program.Inlining is a highly resilient transformation (it is essentially one-way),since once a procedure call has been replaced with the body of the called procedure and the procedure itself has been removed,there is no trace of the abstraction left in the code.Outlining(turning a sequence of statements into a sub-routine)is a very useful companion transformation to inlin-ing.Figure6shows how procedures and are inlined at their call-sites,and then removed from the code.Sub-sequently,we create a bogus procedural abstraction by ex-tracting the end of’s code and the beginning of’s code into a new procedure.In object-oriented languages such as Java,inlining may, in fact,not always be a fully one-way transformation.Con-sider a method invocation.The actual procedure called will depend on the run-time type of.In cases when more than one method can be invoked at a particu-lar call site,we have to inline all possible methods[6]and select the appropriate code by branching on the type of. Hence,even after inlining and removal of methods,the ob-fuscated code may still contain some traces of the original abstractions.5.3Clone methodsWhen trying to understand the purpose of a subroutine a reverse engineer will of course examine its signature and body.However,equally important to understanding the behavior of the routine are the different environments in which it is being called.We can make this process more difﬁcult by obfuscating a method’s call sites to make it ap-pear that different routines are being called,when,in fact, this is not the case.Figure7shows how we can create several different ver-sions of a method by applying different sets of obfuscating transformations to the original code.We use method dis-patch to select between the different versions at runtime. 6Obfuscating built-in data typesIn this section we will present transformations that ob-scure the basic data types(such as integers and strings)01234590123451901210123401234012345629 012341used in the source application.Generally,designing such transformations is difﬁcult since these types form such an integral part of most programming languages.For this very reason the transformations are often high in cost and low in stealth.Nevertheless,combined with other transformations these obfuscations can sometimes be quite effective.6.1Split variablesBoolean variables and other variables of restricted range can be split into two or more variables.We will write a variable split into variables as.Typically,the potency and resilience of this transformation will grow with.Unfortunately,so will the cost of the transformation,so we usually restrict to2or3. To allow a variable of type to be split into two vari-ables and of type requires us to provide three pieces of information:(1)a function that maps the values of and into the corresponding value of,(2)a function that maps the value of into the corresponding val-ues of and,and(3)new operations(corresponding to the primitive operations on values of type)cast in terms of operations on and.In the remainder of this section we will assume that is of type boolean,and and are small integer variables.Figure8(a)shows a possible choice of representation for split boolean variables.The table indicates that boolean variable has been split into two short integer variables and.If or then is, otherwise,is.Given this new representation,we have to devise substi-tutions for the built-in boolean operations(). The easiest way is simply to provide a run-time lookup table for each operator.Tables for and are shown in Figure8(c)and(d),respectively.Given two boolean vari-Figure5:The Java method on the left is obfuscated by translating it into the bytecode.This code is then executed by a stack-based interpreter specialized to handle this particular virtual machine code.This is akin to Proebsting’s superoperators[16].To increase the resilience of this transformation,isﬁrst obfuscated by inserting a bogus if-statement whose opaque predicate(which depends on two un-aliased pointer variables and)will always evaluate to.Even after deobfuscating the interpreter,the resulting code is still obfuscated.ables and,is computed as.In Figure8(e)we show the result of splitting three boolean variables,,and .An interesting aspect of our chosen represen-tation is that there are several possible ways to compute the same boolean expression.Statements(3’)and(4’)in Fig-ure8(e),for example,look different,although they both as-sign to a variable.Similarly,while statements(5’) and(6’)are completely different,they both compute.The potency,resilience,and cost of this transformation all grow with the number of variables into which the origi-nal variable is split.The resilience can be further enhanced by selecting the encoding at run-time.In other words,the run-time lookup tables of Figure8(b-d)are not constructed at obfuscation-time(which would make them susceptible to static analyses)but by algorithms included in the obfus-cated application.This,of course,would prevent us from using in-line code to compute primitive operations,as done in statement(6’)in Figure8(e).Figure7:Cloning methods.and have been generated by applying different obfuscating transformations to the body of.The calls and look as if they were made to two different methods,while in fact they go to different-looking methods with identical behavior.is a buggy version of that is never called.1 0012303013220133013122110(a)(b)(c)(d)(e)Figure8:Variable splitting example.Tables(b-d)are used to compute boolean operations.They are either constructed at obfuscation-time and stored as static data in the obfuscated application,or generated at run-time by the obfuscated application itself.Figure9:A function producing the the strings,,and.Note that this type of code cannot be coded directly in Java,since the language lacks s.It can,however,be coded at the bytecode level.(a)(b)Figure10:Merging two32-bit variables and into one64-bit variable.occupies the top32bits of,the bottom32 bits.If the actual range of either or can be deduced from the program,less intuitive merges could be used.(a)gives rules for addition and multiplication with and.(b)shows some simple examples.The example could be further obfuscated,for example by merging and into.。